# How to complete an average speed question? Find the average speed of the trip there.I have no idea how to go about solving these questions (on my summer math packet); Jak left Aly's house and...

How to complete an average speed question? Find the average speed of the trip there.

I have no idea how to go about solving these questions (on my summer math packet); Jak left Aly's house and traveled toward town. 1 hour later Ry left traveling 10km/h faster to catch up to him. After 2 hours Ry finally caught up. Find Jak's average speed. James drove to the trin station and back. The trip there took four hours and the trip back took five hours. He averaged 28 mph on the return trip. Find the average speed of the trip there.

Expert Answers
embizze | Certified Educator

For each of these problems you will use the formula `d=rt` where d is the distance, r the rate, and t the time.

I can only answer 1 problem, but I can tell you how to set them up as each of these questions follows the same basic pattern. In each case, you either know the distance, or you know that the distance travelled by the two parties is the same.

In the first question, Jak travels a distance `d` in time `t=3` hours. (It took Ry 2 hours to catch him, and Ry leaves 1 hour later than Jak thus 1+2=3). Let Jak's rate be `x` `("km")/("hr")` . Then Ry's rate is `x+10 ("km")/("hr")` and the time he travelled is `t=2` hours.

For Jak we have `d_1=rt=x3` and for Ry we have `d_2=(x+10)2` where `d_1` is the distance Jak travels, and `d_2` is the distance Ry travels. But they meet up, and since they started from the same place they travelled the same distance or `d_1=d_2` .

This implies that `3x=2(x+10)` (Set the expressions for `d_1,d_2` equal to each other). Solving this yields x=20.

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Jak travels at an average rate of 20 `("km")/(:hr")`

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Checking we see that this means Ry travels at `30 ("km")/("hr")` (20+10=30); Jak will have travelled 3(20)=60km while Ry will have travelled 2(30)=60km so that they meet 60km from Aly's house.

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Set up the other questions in a similar manner. You will have two equations in the form d=rt, but you will find that the distance in each case is the same, or that you are given the distance.

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