Question

A crew can row 10 miles in \(\frac{5}{6}\) th of an hour down-stream and 12 miles upstream in 90 minutes. Find the current's rate and crew's rate in still water.

• A. 12 mph, 4 mph
• B. 10 mph, 2 mph
• C. 8 mph, 4 mph
• D. 12 mph, 2 mph

Answer 1

The Correct Option is B

To find the current's rate (\(c\)) and the crew's rate in still water (\(b\)), we form two equations based on the given information:

• Downstream: Speed = \(b + c\). They row 10 miles in \(\frac{5}{6}\) hour, so:
  \(b + c = \frac{10}{\frac{5}{6}} = \frac{10 \times 6}{5} = 12\) mph
• Upstream: Speed = \(b - c\). They row 12 miles in 90 minutes (1.5 hours), so:
  \(b - c = \frac{12}{1.5} = 8\) mph

We now have the system of equations:

1. \(b + c = 12\)
2. \(b - c = 8\)

Adding these equations to eliminate \(c\):

\(b + c + b - c = 12 + 8\)

\(2b = 20\)

Therefore, \(b = \frac{20}{2} = 10\)

Substitute \(b = 10\) into the first equation:

\(10 + c = 12\)

\(c = 12 - 10 = 2\)

The crew's rate in still water is \(b = 10\) mph and the current's rate is \(c = 2\) mph. The correct answer is 10 mph, 2 mph.