Question

two trains start from towns 240 mi apart and travel towards each other on parallel tracks. they pass each other 1.6 hr later. If one train travels 10 mph faster than the other, find the speed of each train

Answer 1

240 miles total
pass 1.6 hours later

A = train A's speed
B = train B's speed

A = B+10 (given)

If they pass 1.6 hours after starting, that means after 1.6 hours they together have covered the entire 240 miles; since A and B are speeds in units (mph),

A (1.6) + B (1.6) = 240

Substitution, using [A=B+10]

(B+10)(1.6) + B(1.6) = 240

B(1.6) + (16) + B(1.6) = 240

B(3.2) + (16) = 240

B(3.2) = 224

B = 70

Then substitute that into the equation A=B+10 to find that train A moved at 80mph.

So train A's speed is 80 mph and train B's speed is 70 mph.

To check, see how far each goes in 1.6 hours:

Train A: 80(1.6) = 128 miles
Train B: 70(1.6) = 112 miles

Adds up to 240!

Answer 2

thank you very much screencapping for future reference on these types of problems