Answer:
20 mph
Step-by-step 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
[tex]\frac{350}{v_{b} + 30}=\frac{140}{v_{b}}[/tex]
Cross multiply
[tex]350v_{b} = 140(v_{b} + 30)\\\\350v_{b} = 140v_{b} + 4200\\\\350v_{b} -140v_{b} = 4200\\\\210v_{b} = 4200[/tex]
Divide both sides by 210
[tex]\frac{210v_{b} }{210} \frac{4200}{210} \\\\v_{b} = 20 mph[/tex]
