Rate-Distance-Time Problems?

Question

Exactly 40 minutes after the Goodsons head south on the highway, the Claytons set out from the same point and follow the same route. The Goodsons travel at 45 mi/h. The Claytons travel at 60 mi/h. How long does it take the Claytons to overtake the Goodsons?

An Explanation would be nice. Thank you.

Answer 1

In 40 minutes, the Goodsons will travel 45 mi/h * 40/60 (40 minutes out of 60 minutes in an hour):

so the Goodsons have travelled 30 miles...

Since the Goodsons are travelling 45 MPH, and the Claytons are travelling 60 MPH, they are closing at a rate of 15 MPH.

Since the Claytons have to close a distance of 30 miles and are closing at 15 miles each hour, it will take them 2 hours to close 30 miles.

Answer 2

For this type of problem, I always find that drawing a picture helps.

C-----------G
^^^ this is the distance G travels in 40 minutes

Another way to ask this question is:
How fast will the Claytons will be closing on the Goodsons?

Given what we know G traveling at 45 mph and C traveling behind them at 60 mph

60mph - 45mph = 15 mph

Figure out how far G goes in 40 minutes (they started first)

then all you have to do is figure out how long it takes to cover that distance traveling at 15mph.

Answer 3

You know that rate x time =distance.
In this case, the distance is the same, so
Rgoodsons xTgoodsons = R claytons x T claytons
(45) x (T) = (60)(T-40)
45T = 60T -2400
-15T = -2400
T = 160 minutes
Claytons time = 160-40 = 2 hours