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

average speed to mexico = 172 mi/4 hr
train speed = 50 mi/hr
bus speed = 30 mi/hr

50m/hr * tt + 30mi/hr * tb = 172 hrs, where tt = time on train, tb = time on bus
tt50 + tb30 = 172 miles
tb + tt = 4 hrs

Ans. tt = 13/5 hrs and tb = 7/5 hrs

Answer 2

Here is slightly different way to look at it.

train_dist = train_rate * train_time
bus_dist = bus_rate * bus_time

train_dist + bus_dist = 172
Therefore: (train_rate * train_time) + (bus_rate * bus_time) = 172

Let x = train_time, then (4-x) = bus_time.
Now substitute in the variables and the rates and you will have:
(50 * x) + (30 * (4-x) ) = 172
50x + 120 -30x = 172
- 120 -120
-----------------------
20x = 52

x = (52/20) = 13 / 5 = 2.6 hours

Answer 3

r t = d
Solve the following for t, the time on the train:
50 t + (4 - t) 30 = 172
t = 13/5 hours or 2hours and 36 minutes