SOLUTION: A train travels 180 miles in the same time that a car travels 120 miles. The speed of the train is 20 miles per hour faster than the speed of the car. Find the speed of the train a

Algebra ->  Equations -> SOLUTION: A train travels 180 miles in the same time that a car travels 120 miles. The speed of the train is 20 miles per hour faster than the speed of the car. Find the speed of the train a      Log On


   

Question 159703: A train travels 180 miles in the same time that a car travels 120 miles. The speed of the train is 20 miles per hour faster than the speed of the car. Find the speed of the train and the speed of the car. Please solve step by step.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
We know that d=rt and therefore t=d%2Fr. Now, if d%5Bt%5D and r%5Bt%5D are the distance travelled and the speed of the train, while d%5Bc%5D and r%5Bc%5D are the distance travelled and the speed of the car, then:
We are given that:
d%5Bt%5D=180,

d%5Bc%5D=120,

and r%5Bt%5D=r%5Bc%5D%2B20

Further, we know that the time is the same for both the train's trip and the car's trip.

For the train: t=180%2Fr%5Bt%5D or t=180%2F%28r%5Bc%5D%2B20%29 and

For the car: t=120%2Fr%5Bc%5D

Since t=t, we can say 180%2F%28r%5Bc%5D%2B20%29=120%2Fr%5Bc%5D

Cross-multiply: 180r%5Bc%5D=120%28r%5Bc%5D%2B20%29

Distribute: 180r%5Bc%5D=120r%5Bc%5D%2B2400

Add -120r%5Bc%5D to both sides: 180r%5Bc%5D-120r%5Bc%5D=2400

Collect like terms: 60r%5Bc%5D=2400

Divide by 60: r%5Bc%5D=40

Compute r%5Bt%5D: r%5Bt%5D=r%5Bc%5D%2B20=40%2B20=60

So the train travels at 60 mph and the car at 40 mph.

Check the answer:

How long does it take the train to go 180 miles? 180%2F60=3 hours

How long does it take the car to go 120 miles? 120%2F40=3 hours.

The time is the same so the answer checks.