Question

A motorboat takes hours to travel kilometers going upstream. The return trip takes hours going downstream. What is the rate of the boat in still water and what is the rate of the current

Answer 1

Rate of boat in still water = 56 km per hour

Rate of the current = 8 km per hour

Explanation:

This question is incomplete; to understand how to solve these questions let the question is,

A motorboat takes 4 hours to travel 192 km going upstream. The return trip takes 3 hours going downstream. What is the rate of the boat in still water and what is the rate of current.

Let the rate of current = u km per hour

And the rate of boat in still water = v km per hour

Then going upstream, rate of the boat = Rate of the boat in still water - Rate of current

= (v - u) km per hour

Similarly, going downstream, rate of the boat = Rate of boat in still water + Rate of current

= (v + u) km per hour

Since, the boat takes 4 hours upstream,

By using the formula,

Rate =
`\frac{\text{Distance}}{\text{Time}}`

Distance traveled = Rate × Time

For upstream,

192 = 4(v - u)

v - u = 48 ------(1)

For downstream,

192 = 3(v + u)

v + u = 64 ------(2)

By adding equation (1) and (2),

(v - u) + (v + u) = 48 + 64

2v = 112

v = 56 km per hour

From equation (1),

56 - u = 48

u = 56 - 48

u = 8 km per hour

Rate of boat in still water = 56 km per hour

Rate of the current = 8 km per hour