Can you help answer the word problem?

Question

Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels at 90 miles per hour. The westbound train travels at 80 miles per hour. How long will it take for the two trains to be 408 miles apart?

Answer 1

I love these questions and they are actually very easy and just require practice.

 

You know that D = R * T is your formula and you have it twice and just need to manipulate it.

 

2 things you know to start, the T is the same for both trains, and the D1 + D2 = 408.

 

Your first train is D1 = 90 * T

 

Your second train is D2 = 80 * T

 

Remember your D1 + D2 = 408 so let's solve for D1

 

D1 = 408 - D2

 

Now go back to your first equation is substitute

 

408 - D2 = 90 * T

 

Guess what, you have D2 already in terms of T on your second equation so let's substitute again and solve for T

 

408 - (80 * T) = 90 * T

 

408 - 80*T = 90*T

 

408 = 170*T

 

T = 408/170

 

T = 2.4 and that is in hours

 

ALWAYS go back and check by putting your answer in each original equation

 

D1 = 90*T

D1 = 90*2.4 = 216 miles

 

D2 = 80*T

D2 = 80*2.4 = 192 miles

 

216+192 = 408 miles!

 

All the best

 

Lori