Speed, Time and Distance Formulas

Boyet B. Aluan

San Roque Elementary School

What are Time and Distance formulas? Time and Distance

Formulas relate time, distance, and speed. These relationships have many practical applications.

Why do you need to know the Speed, Time and Distance Formula? To figure how long a trip will

take To see how far you can go in

a set amount of time To see how fast you took a trip To compare different trips

Steps in solving Speed, Time and Distance Formulas Step 1. Translate the question

into mathematical terms. For example, if you are asked miles per hour, write the question as miles divided by hours.

Ex m/h or mph

Steps in solving Speed, Time and Distance Formulas Step 2. Put everything in

constant units. For example, if the question asks miles per hour, every time must be placed in terms of hours, and every distance must be placed in terms of miles.

Conversion Units

Remember: There are 60 seconds in a minute, 60 minutes in an hour, and 24 hours in a day.

Remember: There are 12 inches in a foot, 3 feet in a yard, and 5280 feet in a mile.

Time Conversions

To convert minutes to hours, divide by 60. To convert hours to minutes, multiply by 60 To convert seconds to minutes, divide by 60 To convert minutes to seconds, multiply by

60 To convert days to hours, multiply by 24 To convert hours to days, divide by 24

Measurement Conversions

To convert inches to feet, divide by 12 To convert feet to inches, multiply by 12 To convert feet to miles, divide by 5280 To convert miles to feet, multiply by 5280

Step 3. Write the equation you want to solve.

Use the correct formula to solve it. Be careful about what you multiply,

and what you divide!

What are the basic formulas?

Distance = Rate * Time (d = r * t) Rate = Distance / Time (r =d/ t) Time = Distance / Rate (t = d / r)

Be sure you use the right formula!

To find distance

Distance = Rate * Time (d = r * t)

For example, to find miles, multiply miles per hour (rate) times the number of hours.

Miles = Miles x Hours

Hours

The hours cancel, you are left with miles.

To find the rate of speed

Rate = Distance /Time (r =d/ t)

rate- constant/ average speed. To find miles per hour, divide miles driven by the number of hours driven.

To find the time it takes to travel. Time = Distance / Rate (t = d / r)

Hours = Miles_____

Miles/Hour

Remember, to divide fractions, flip and multiply

Hours = Miles x Hours

Miles

Miles cancel, you are left with hours

Quiz 1-finding the distance

A girl cycles for 3h at a speed of 40 km/h. what is the distance did she travel?

Step one

Put in constant unitsRate was given in km/h,

Question 1What formula should be used? We are looking for distance so use

Answer A. d=r*t B. r=d/t C. t=d/r

Solve

D=rt

D=?

R=40km/h

T=3hrs

Substitute the value

D=rt

D=40km/h(3h)

Cancel h

D=120km

Quiz2 finding the time

A train travels at a speed of 30mph and travel a distance of 240 miles. How long did it take the train to complete its journey?

Question 1What formula should be used? We are asked to find how long did it

take the train to complete its journey so used

Answer A. d=rt B. r=d/t C. t=d/r

Solve

T=d/r

T=?

R= 30mph

D=240m

T= 240M/30mph

Cancel m(miles)

T=8h is the time to complete the journey

Quiz 3

A car travels a distance of 540km in 6 hours. What is the speed did it travel at?

Question 3

We are asked to find the rate to travel the distance of 540km in 6 hours. What formula should be used?

Answer A. d=rt B. r=d/t C. t=d/r

Solution

R=d/t

R=?

D= 540 m

T=6h

Substitute:

R=d/t

R=(540m)/6h

R=90mph

Quiz4

John is a runner. He runs the 100m sprint in 10.6s. What speed did he travel at? The unit is (m/s)Use r=d/t where r=?, t=10.6s, d=100meterSubstituteR=(100m)/10.6sR= 9.43m/s

Quiz 5

At 11:00 am, a car(1) leaves city “A” at a constant rate of 60m/h toward city “B”. At the same time a second car(2) leaves city “B” toward city “A” at the constant speed of 50mph. The distance between city A and B is 220miles and these cities are connected by a highway used by the two cars. At what time will the two cars cross each other?

Solution -construct a tabular presentation

Speed (R) TIME (T) Distance (D)

Car 1 60mph

car2 50mph

total 110mph ? 220m

T=d/tT=220m/110mphT=2hSo at constants speed, cars cross each other at 1:00pm

Quiz 6

Kali left school and traveled toward her friend’s house at an average speed of 40km/h. Matt left one hour later and traveled in the opposite direction with an average speed of 50km/h. find the number of hours Matt needs to travel before they are 400km apart.

Solution-construct tabular presentation

1st hour 2nd hour 3rd hour 4th hour 5th hour total

Kali

Matt -left

total 40

From the table, Matt needs 4 hours so they can be 400km apart

40 4040 40 40

50 505050 200

200

400km

Quiz 7 Chelsea left the White House and

traveled toward the capital at an average speed of 34km/h. Jasmine left at the same time traveled in the opposite direction with an average speed of 65km/h. Find the number of hours Jasmine needs to travel before they are 59.4 km apart.

Solution

R=34km/h+64km/h=99km/h

D=59.4km

T=?

T=d/r

T=59.4km/99kmph

T=0.6h

Speed Time Distance

Chelsea 34km/h ?

Jasmin 64km/h ?

total 99km/h ? 59.4km apart

Quiz 8

A train leaves Deb’s house and travels at 50mph. Two hours later, another train leaves from Deb’s house on the track beside or parallel to the first train but it travels at 100mph. How far away from Deb’s house will the faster train pass the other train?

Solution

Since their distance is equal, Let n-time takes faster train to take the distance

N+2-time takes slower train to cover the distance Thus 50(n+2)=100n 50n+100=100n-distibutive property -100n+50n=-100-transposition -50n=100 (-50n/-50)=-(100/-50)-cancelation/property of sign

numbers N=2

Speed Time Distance

Slower train 50kmph N+2 50(n+2)

Faster train 100kmph n 100n

total

So means, by substitution method

=100n

=100(2)

=200km

The faster train is at 200miles away from slower train.

Quiz 9

A train left Chicago and traveled towards Dallas. Five hours later another train left for Dallas traveling at 40mph with a goal or catching up with the first train bounded for Dallas. The second train finally caught up with the first train after traveling for three hours. How fast was the train that left first going?

Solution –Completing the table/graph

Since 2nd train speed is 40mph travelled for 3h..

D=rt D=40mph*3h D=120m

Speed Time distance

1st train 15mph 5+3 120miles

2nd train 40mph 3 120miles

Thus 1st train d=120m T=3h+5h

R=d/t R=120m/8h R=15mph

Quiz 10.Catching up same direction, has equal distance! A jet took off Toronto, heading west at a

speed of 405mph. Another jet left for Toronto from the same airport sometime after the first jet took off and it was traveling at a speed of 486mph. Ten hours later, the second jet caught up with the first jet. How long did the jet fly before the second jet caught up?

Solution

405(n+10)=4860 405n+4050=4860 405n=4860-4050 405n=810 405n/(405)=810/(405) N= 2

Speed Time Distance

Jet1 405mph n+10 405(n+10)

Jet2 486mph 10h 4860mph

So n+10 =2+10 =12 Time =12h 1st jet took 12h before it

just get caught.

Thanks!!!

Boyet B. Aluan