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A boat travels upstream and reaches Town A in 2 hours. The return trip is 1 h 20 min. What is the speed of the boat in still water if the speed of the stream is 3 mph? a) 5 mph b) 7 mph c) 9 mph d) 12 mph

User Snukus
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If a boat travels upstream and reaches Town A in 2 hours. the speed of the boat in still water is: D. 12 mph.

What is the speed?

Let denote the speed of the boat in still water as B and the speed of the stream as S.

The speed of the boat relative to the ground is:

Speed upstream = B - S

The speed of the boat relative to the ground is given by:

Speed downstream = B + S

The return trip takes 1 hour and 20 minutes which is equivalent to 1.33 hours.

Set up two equations:

Equation 1: Speed upstream × Time upstream = Distance

Equation 2: Speed downstream × Time downstream = Distance

Since the distance traveled in both directions is the same set the two equations equal to each other:

(B - S) × 2 = (B + S) × 1.33

Solve for B which is the speed of the boat in still water:

2B - 2S = 1.33B + 1.33S

2B - 1.33B = 2.66S

0.67B = 2.66S

B = 2.66S / 0.67

Substitute :

B = 2.66 × 3 / 0.67

B = 11.94 mph

B-= 12 mph

Therefore the speed of the boat in still water is approximately 12 mph.

User Pradyuman
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