Uniform Motion Question

Question

A motorboat can maintain a constant speed of 16 mph relative to the water. The boat makes a trip upstream to a certain point in 20 minutes; the return trip takes 15 minutes. What is the speed of the current?

Answer 1

Fiona from the land of Microsoft,

 

Let x be the unknown speed of the current flowing down stream.  Then,

(16 - x) is the average speed of the motorboat relative to the river bank heading upstream and fighting the current

(16 + x) is the average speed relative to the river bank coming back downstream when the current is helping

The distance, d(t) traveled in time t is measured on the river bank and is the same whether going there or coming back

The time of travel is however different because the current either slows down or speeds up the motor boat

 

Then d = st is the distance formula, but must use compatible units in all the variables

Hence d is in miles, s is in mph, and t is in hours, not minutes!

 

Going upstream:         d = (16-x)(20/60) = (1/3)(16-x)

Coming downstream:  d = (16+x)(15/60) = (1/4)(16+x)

The distances are equal since the starting and ending points are on the riverbank.

 

So (1/3)(16-x) = (1/4)(16+x)  & multiplying left and right sides by 12 , we get rid of the fractions

So 4(16-x) = 3(16+x)  and distributing/expanding:  64 - 4x = 48 + 3x

And 16 = 7x, so 

x = 16/7 mph or 2.286 mph