Question

3. A boat takes 6.5 hours to make a 70-mile trip upstream and 5 hours on the 70-mile return trip. Let v be the speed of the boat in still water, and c be the speed of the current. The upstream speed of the boat is v – cand the downstream boat speed is v + c. 2. Write two equations, one for the upstream part of the trip and one for the downstream part, relating boat speed, distance, and time. b. Solve the equations in part a for the speed of the current Round your answer to the nearest tenth of a mile per hour and show your work

Answer 1

6.5 hours to make a 70 mile trip upstream

5 hours tomake 70 miles downstream

v = speed of boat

c = speed of current

Upstream speed = v - c

Downstream speed = v + c

In general: velocity = diatance/time

In this case, when going upstream:

v - c = 70/6.5

When going downstream:

v + c = 70/5

From the first equation, we can get the value of v:

v = 70/6.5 + c

Using this value on the second equation:

(70/6.5 + c) + c = 70/5

Solving for c:

10.7692 + 2c = 14

2c = 14 - 10.7692 = 3.2308

c = 3.2308/2 = 1.6154

c = 1.6154

Using this value on the equation for v:

v = 70/6.5 + c = 70/6.5 + 1.6154 = 12.3846

v = 12.3846

Answer:

Speed of the boat: 12.3846 miles per hour

Speed of the current = 1.6154 miles per hour