Question

The speed of a boat is 16 mph and the rate of flow of the river is 4 mph. As it cruised downstream, the boat traveled 120 miles, everything else being constant. What distance will the boat cover during the same time, going upstream?
A. 82 miles
B. 72 miles
C. 57 miles
D. 98 miles

Answer 1

To find the distance the boat will cover going upstream, we first need to calculate the time it takes for the boat to travel downstream.

**Downstream:**
The effective speed of the boat when cruising downstream is the sum of the boat's speed and the river's current speed:

\[
\text{Downstream speed} = \text{Boat speed} + \text{River speed} = 16 \text{ mph} + 4 \text{ mph} = 20 \text{ mph}
\]

Now we can calculate the time taken to travel 120 miles downstream:

\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{120 \text{ miles}}{20 \text{ mph}} = 6 \text{ hours}
\]

**Upstream:**
Next, we'll calculate how far the boat can travel upstream during this same time. The effective speed of the boat going upstream is the boat's speed minus the river's current speed:

\[
\text{Upstream speed} = \text{Boat speed} - \text{River speed} = 16 \text{ mph} - 4 \text{ mph} = 12 \text{ mph}
\]

Now we can find the distance covered upstream in 6 hours:

\[
\text{Distance} = \text{Speed} \times \text{Time} = 12 \text{ mph} \times 6 \text{ hours} = 72 \text{ miles}
\]

Therefore, the distance the boat will cover while going upstream is **72 miles**.

Thus, the answer is:

**B. 72 miles**