Question

Algebra 112Unit 1 - Mathematical MindsetsName:Big Idea: Rate Problems1. A freight train left Pennsylvania Station traveling at 35 mph. Two hours later, a high speed train leftPennsylvania Station on parallel tracks traveling 55 mph.a) How many hours after the slow train left will it take the fast train to catch up with the slow train?b) How far will the fast train have traveled when it caught up with the slow train?TrainRateTimeDistanceFreightHigh Speed

Answer 1

a) 3.5 hours

b)192.5 miles

Step-by-step explanation:

I will call the freight train Train 1, and the high speed train Train 2.

Speed of train 1: 35 mph

Speed of train 2: 55mph

We calculate the difference in speeds:

`55mph-35mph=20mph`

To solve, we need to know how far are the trains from each other when the train 2 starts.

Since its 2 hours later, And the train 1 travels at 35mph (35 miles in 1 hour), in two hours the train 1 is 35*2=70miles away from the starting point.

The train 2 need to recover this distace, since the difference in their speed is 20mph, this is the relative speed of the second train regards to train 1.

No we calculate, at 20mph (the relative speed) in how much time the train 2 will travel the 70 miles that separates them.

We do the following:

`\frac{70\text{miles}}{20\text{mph}}=3.5h`

a) It takes 3.5 hours for the fast train to catch up with the slow train

To solve b) we use the speed of train 2: 55mph (travels 55 miles in 1 hour), and since it traveled for a time 3.5 hours:

`55\text{mph(3.5h)}=192.5\text{miles}`

b) The fast train teveled 192.5 miles when it caught up with the slow train.