A motorboat maintained a constant speed of 14 miles per hour relative to the water in going 33 miles upstream and then returning. The total time for the trip wa

Question

A motorboat maintained a constant speed of 14 miles per hour relative to the water in going 33 miles upstream and then returning. The total time for the trip was 7.0 hours. Use this information to find the speed of the current.

Answer 1

Construct the equations as

(14 − C) miles per hour × (T) hours = 33 miles.

(14 + C) miles per hour × (7 − T) hours = 33 miles.

Equate the left sides of these equations to obtain

14T − CT = 98 + 7C − 14T − CT.

Reorganize as

28T = 98 + 7C, which goes to

4T = 14 + C or T = 3.5 + 0.25C.

Go to (14 − C) miles per hour × (T) hours = 33 miles

and build

(14 − C) miles per hour × (3.5 + 0.25C) hours = 33 miles.

Rewrite this last as 49 + 3.5C − 3.5C − 0.25C² = 33.

Reorganize as 0.25C² − 16 = 0 which gives C = 8 miles per hour and Time Upstream as 5.5 hours.

Then Time Downstream is (7 − 5.5) or 1.5 hours at Speed (14 + 8) miles per hour.

Confirm that (14 − 8) × 5.5 and (14 + 8) × 1.5 both equal 33.