Question

Train a is traveling at 30 mph faster than train b. If train a travels 350 miles in the same amount of time that train b travels 140 miles how fast is train b traveling

Answer 1

20 mph

Explanation:

Let speed of Train a = Va mph

Let speed of Train b = Vb mph

Va = Vb + 30

Let time taken for Train a = Ta

Let time taken for Train b = Tb

time taken = distance travelled/speed

Ta = 350/Va = 350/(Vb+30)

Tb = 140/Vb

But they both travel in the same amount of time.

So, Ta = Tb

`(350)/(v_(b) + 30)=(140)/(v_(b))`

Cross multiply

`350v_(b) = 140(v_(b) + 30)\\\\350v_(b) = 140v_(b) + 4200\\\\350v_(b) -140v_(b) = 4200\\\\210v_(b) = 4200`

Divide both sides by 210

`(210v_(b) )/(210) (4200)/(210) \\\\v_(b) = 20 mph`