Question

Jerry and Milton set out for a ride in the hill country at 30 mph. Their car broke down and they caught a ride back home in a truck at 20 mph. If they were gone for 10 hours, how far from home did the breakdown occur?

Answer 1

Their car broke down 120 miles from home.

• Let d be Jerry and Milton's distance from home where their car broke down.

• Let t be the time it takes to travel to d with a speed of 30 mph.

• Let t' be the time it takes to travel back home at 20 mph.

Finding the required equations

Since both distances to and fro are the same, we have that

30t = d (1) and 20t' = d (2)

30t = 20t'   (3)

Also, since they wer gone for 10 hours, we have that t + t' = 10 (4)

So, t' = 10 - t

Solving for t

Substituting t' into (3), we have

30t = 20(10 - t)

30t = 200 - 20t

30t + 20t = 200

50t = 200

t = 200/50

t = 4 hours.

Solving for d

Substituting t into (1), we have

d = 30t

= 30 × 4

= 120 miles

So, their car broke down 120 miles from home.

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