Question

Jack is traveling in a boat that takes 30 minutes to cover 18 miles downstream. The ratio of the speed of the boat in still water to the speed of the stream is 5:1. How much time will it take to cover 20 miles upstream?

• A. 40 min
• B. 50 min
• C. 60 min
• D. 30 min

Answer 1

The correct option is B 50 min

Let's find the speed in the downstream.

$\text{Downstream speed}=\frac{\text{Distance traveled}}{\text{Time}}\times 60$

$=\frac{18}{30}\times 60$

$=36mph$

It is given that the ratio of the speed of the boat in still water to the speed of the stream is 5:1.

Let the speed of the boat in still water and the speed of the stream be 5x and x, respectively.

We know,
Downstream speed = Speed of the boat in still water + Speed of the stream

⇒ Downstream speed = 5x + x

⇒ Downstream speed = 6x

And,
Upstream speed = Speed of the boat in still water – Speed of the stream

⇒ Upstream speed = 5x – x

⇒ Upstream speed = 4x

We know,
Downstream speed = 36

So,

$6x=36$

$\Rightarrow x=\frac{36}{6}$

$\Rightarrow x=6$

So,

$\text{Upstream speed}=4x=4\times 6=24\text{mph}$

$\text{Time taken to travel 20 miles upstream}=\frac{\text{Distance traveled}}{\text{Speed}}\times 60$

$=\frac{20}{24}\times 60=50\text{min}$