Distance and Time

Question

Miguel is traveling to Mexico. He travels for 3 hours for a total of 101 miles. He first travelled by train, going 40 mph, then took the rest of the trip by bus, going 30 mph. How long was he on the train?

Answer 1

In order to solve this problem, we will need two equations.

We know that distance D = rate R x time T

let x =  the time at 40m/h, and y = the time at 30m/h

then, D = 40m/h · x + 30m/h · y

we also know the x + y = 3h; solving this equation for x, we get 3 - y = x

we then substitute that value into the first equation, which yields 101m = 49m/h · (3 - y) + 30m/h · y

that equation becomes 101m = 120 -40y +30y, which becomes -19 = -10y, which yields y = 1.9h

replacing 1.9h for y in the equation x + y 3h, we get x = 1.1h

 

so, the answer is 1.1 hours at 40m/h and 1.9 hours at 30m/h

 

Proof: 40m/h · 1.1h = 44m, and 30m/h · 1.9h = 57m; 44m + 57m = 101m