IXL - Rate of travel: word problems (Algebra 1 practice)

Two friends are windsurfing at a popular beach. Shawna is paddling out on her board, going 3 miles per hour. At the same time, 2 miles directly in front of Shawna, Peter has caught a big wave and is riding it back in at a rate of 15 miles per hour. In how much time will the two surfers pass each other?

If necessary, round your answer to the nearest minute.

hours and minutes

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Learn with an example

question

Two freight trains leave the station in Allenville at the same time. The first train is headed due south at a speed of 43 kilometers per hour. In comparison, the second train is going due north at 64 kilometers per hour. In how long will the trains be 450 kilometers apart?

If necessary, round your answer to the nearest minute.

hours and minutes

key idea

The equation that relates distance, rate (speed), and time is

When two bodies are moving toward each other or away from each other, r is the sum of the rates.

solution

The distance to be covered is 450 kilometers.

The first train's rate is 43 kilometers per hour. The second train's rate is 64 kilometers per hour. Together, they are increasing the gap between them at a rate of

107

kilometers per hour.

Now write an equation and solve for

450

Plug in

450

and

107

Plug in

450

and

107

4.205607…

Divide both sides by 107

The units for t are hours. Convert the units to hours and minutes, rounded to the nearest minute.

The whole-number portion is 4. That is 4 full hours.

Convert the decimal portion.

0.205607…

≈

So, t is approximately 4 hours and 12 minutes.

The trains will be 450 kilometers apart in about 4 hours and 12 minutes.

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Work it out

Not feeling ready yet? These can help:

DD.2Convert mixed time units

X.10Interpret graphs of proportional relationships

D.8Add, subtract, multiply, or divide two decimals

C.3Round decimals

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