Question

1. Chelsea can paint a fence in 9 hours, and Greg can paint the same fence in 7 hours. How long does it take them to paint the fence if they work together? Round to the nearest tenth.

2. Tom left the mall and drove south. George left 2 hours later driving 36 mph faster to catch up with Tom. After 3 hours, he caught up with Tom. Find Tom’s average speed


72 mph


54 mph


90 mph


36 mph

Answer 1

1. 3.9 hours
2. 90 mph

Explanation:

1.

The sum of the rates of painting, in fences per hour, is ...

1/9 + 1/7 = (9+7)/63 . . . . fences per hour

The total rate in hours per fence is the inverse of that:

63/16 = 3 15/16 ≈ 3.9 . . . hours to paint the fence

__

2.

The relevant relationship is ...

distance = speed × time

Let t represent Tom's speed in miles per hour. Then George's speed is (t-36). They both have traveled the same total distance at the point where Tom catches up.

(2+3)(t-36) = 3t

2t = 180 . . . . . . . add 180-3t

t = 90 . . . . . . divide by 2

Tom's average speed is 90 miles per hour.