Train and TunnelDate: 7/18/96 at 7:32:4 From: Anonymous Subject: Train, Tunnel Length A train passes completely through a tunnel in 5 minutes. A second train, twice as long, passes through the tunnel in 6 minutes. If both trains are traveling at the same speed, 24km/h, determine the length of the tunnel and the lengths of the trains. Date: 7/22/96 at 21:58:24 From: Doctor Luis Subject: Re: Train, Tunnel Length To answer this question you must first define what is meant by a train "passing through a tunnel." Thus, in order to solve this, I will assume that the time it takes for the train to pass through the tunnel is the time interval measured from the instant the front of the train enters the tunnel to the instant the back of the train leaves the tunnel. What is the distance traveled by the front while the train goes "through" the tunnel? Answer: T+L, where L is the length of the train, and T is the length of the tunnel (this is because when the back leaves the tunnel, the front is L meters away from the back). So, the first train (length l) passes the tunnel (length T) in 5 minutes, at 24 km/hr. The distance covered (by the front) is (24 km/hr)*(5 mins)*(1/60 hr/mins)*(1000 m/km) = 2000 m Therefore, T + l = 2000 m The second train (length 2*l) passes the tunnel (length T) in 6 minutes, at 24 km/hr. The distance covered (by the front) is (24 km/hr)*(6 mins)*(1/60 hr/mins)*(1000 m/km) = 2400 m Therefore, T + 2l = 2400 m Now, we have two equations in two unknowns, T + l = 2000 T +2l = 2400 from which the solution follows ( I get: T = 1600 m, l = 400 m ) -Doctor Luis, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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