Question

Two trains leave towns 1490 kilometers apart at the same time and travel toward each other. One train travels 20 km/h slower than the other. If they meet in 5 hours, what is the rate of each train?

Answer 1

the rate of each train is 139 km/h and 159 km/h.

Explanation:

let

v = the rate of the slower train

v + 20 = the rate of the faster train

d = 1490 km the distance that the two train will travel

t = 5 hr the time of the travel

since speed = distance/time => distance = speed*time

v*t + (v+20)t = d

5v + 5(v + 20) = 1490

5v+5(v+20)=1490

Step 1: Simplify both sides of the equation.

5v+5(v+20)=1490

5v+(5)(v)+(5)(20)=1490(Distribute)

5v+5v+100=1490

(5v+5v)+(100)=1490(Combine Like Terms)

10v+100=1490

10v+100=1490

Step 2: Subtract 100 from both sides.

10v+100−100=1490−100

10v=1390

Step 3: Divide both sides by 10.

10v/10 = 1390/10

v = 139km/h

Next

we add 139 to 20

139 + 20 = 159 km/h

the rate of each train is 139 km/h and 159 km/h.