Speed Reading Course

Math Rate Word Problem. Please show and explain the steps on how to complete.?

The problem reads: A passenger train leaves Houston at a speed of 60 km/h. Two hours later a second passenger train leaves Houston going in the same direction as the first train on parallel tracks at 90 km/h. How many hours later will the two trains meet at the same spot?

let’s consider that the two train will meet at a point called A . the distance between houston and this point(A) is D ( D is distance in Km)
after 2 hours the first train will be at a point called B , this train will need delta T hours to arrive to the point A and in this time ( delta T ) the second train will arrive to A then we have
first train : V1 ( speed of the train ) 60km/h
T1 ( time needed by the first train to arrive to point A )
T1 = 2h + deltaT
D ( the distance between houston and the point(A) )
==> v1 = D/T1
60km/h = D / (2h + deltaT)
==> D = 60 * ( 2h + deltaT)
D = 120 + 60*deltaT

second train : V2 ( speed of the train ) 90km/h
T2 ( time needed by the second train to arrive to point A )
T2 = deltaT
D ( the distance between houston and the point(A) )

==> V2 = D/T2
90km/h = D / ( deltaT)
==> D = 90 * deltaT

then we have System of equation with Two unknow

D = 120 + 60*deltaT
D = 90 * deltaT
by substraction
the second from the first
0 = 120 – 30*deltaT
30*deltaT = 120
deltaT = 120/30
deltaT = 4 h

4 hours later the two trains will meet at the same spot A and the distance D will be 360 Km

2007 Audi A6 in Houston, TX 77090

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