A pleasure boat on a river traveled from City A to City C with a stop at City B. On the first part of the trip, the boat traveled at an average speed of 1111 miles per hour. From City B to City C the average speed was 1414 miles per hour. The entire trip covered 200200 miles. How long did the entire trip take if the two parts each took the same number of hours?

the entire trip took 16 hours

Step-by-step explanation:

since the time taken to go from A to B is the same that going from B to C

time = distance A to B / velocity from A to B = distance B to C / velocity from B to C

then denoting T as the time taken, D as distances, v as velocities, 1 and 2 for the A-B path and B-C path respectively:

T = D₁/v₁ = D₂/v₂ → D₂=D₁ * (v₂/v₁)

but also the sum of the distances is the total distance covered Dt, thus

Dt = D₁ + D₂

Dt = D₁ + D₁ * (v₂/v₁) = D₁ * (1 + (v₂/v₁))

D₁=Dt / (1 + (v₂/v₁)) = Dt*v₁ / (v₂+v₁)

thus the time Tt required for the whole trip is

Tt = 2*T = 2*D₁/v₁ = 2/v₁ * Dt*v₁ / (v₂+v₁) = 2*Dt / (v₂+v₁)

replacing values

Tt = 2*Dt / (v₂+v₁) = 2 * 200 miles / (11 miles/h + 14 miles/h) = 16 h

thus the entire trip took 16 hours