Question

Manuel traveled 4 hours nonstop to Mexico, a total of 172 miles. He took a train part of the way, which averaged 50mph, and then took a bus the remaining distance, which averaged 30mph. How long was Manuel on the train (in hours)?

Answer 1

Travelled distance by train = S1
Taken time on bus = T1
S1 = 50 * T1

Travelled distance by bus = S2
Taken time by bus = T2
S2 = 30 * T2

S1 + S2 = 172
50 T1 + 30 T2 = 172
5 T1 + 3 T2 = 17.2

T1 + T2 = 4
3 T1 + 3 T2 = 12

2 T1 = 5.2
T1 = 2.6

T2 = 1.4

2.6 hrs on the train