Question

The president of a company traveled 2000 mi by jet and 200 mi on a prop plane. The rate of the jet was four times the rate of the prop plane. The entire trip took 10 h. Find the rate of the jet. Incorrect: Your answer is incorrect. mph

Answer 1

Using a system of equations and substituting the jet's rate as four times the prop plane's rate, we find that the rate of the jet is 280 mph.

Step-by-step explanation:

To find the rate of the jet, we can use the information given and set up a system of equations based on the rates of travel and the distances. Let's denote the rate of the jet as J and the rate of the prop plane as P. It's given that the rate of the jet is four times the rate of the prop plane, so J = 4P.

Since distance equals rate multiplied by time, we can express the travel times for each part of the trip as 2000/J for the jet and 200/P for the prop plane. The entire trip took 10 hours, leading to the equation 2000/J + 200/P = 10. Substituting J with 4P from the first equation, we can find the rate of the prop plane and then determine the rate of the jet.

System of Equations:

1. J = 4P
2. 2000/J + 200/P = 10

Using the relationship J = 4P, we substitute into the second equation:

2000/(4P) + 200/P = 10

500/P + 200/P = 10

700/P = 10

P = 70 mph (rate of the prop plane)

J = 4P = 4 * 70 mph = 280 mph (rate of the jet)