Question

A boat crew rowed 10.5 miles downstream, with the current, in 1.5 hours. the return trip upstream , against the current , covered the same distance , but took 3.5 hours. find the crew’s rowing rate in still water and the rate of the current

Answer 1

The speed of the boat is 5 miles per hours

The speed of the current is 2 miles per hours .

Explanation:

Given as :

The distance cover by boat downstream = D = 10.5 miles

The time taken by boat to cover D distance = T = 1.5 hours

The distance cover by boat Upstream = d = 10.5 miles

The time taken by boat to cover d distance = t = 3.5 hours

Let The speed of boat = x mph

Let The speed of current = mph

Now, According to question

∵ Speed =
`(Distance)/(Time)`

For Downstream

x + y =
`(D)/(T)`

Or, x + y =
`(10.5)/(1.5)`

Or, x + y = 7 .......A

For Upstream

x - y =
`(d)/(t)`

Or, x - y =
`(10.5)/(3.5)`

Or, x - y = 3 .......B

Now, Solving eq A and eq B

So, (x + y) + (x - y) = 7 + 3

Or, (x + x) + (y - y) = 10

Or, 2 x + 0 = 10

∴ x =
`(10)/(2)`

i.e x = 5 mph

So, The speed of the boat = x = 5 miles per hours

Put the value of x into eq A

∵ x + y = 7

Or, 5 + y = 7

∴ y = 7 - 5

i.e y = 2 mph

So, The speed of the current = y = 2 miles per hours

Hence, The speed of the boat is 5 miles per hours and The speed of the current is 2 miles per hours . Answer