Anu26 wrote:
Bunuel wrote:
carcass wrote:
Train A traveling at 60 m/hr leaves New York for Dallas at 6 P.M. Train B traveling at 90 m/hr also leaves New York for Dallas at 9 P.M. Train C leaves Dallas for New York at 9 P.M. If all three trains meet at the same time between New York and Dallas, what is the speed of Train C if the distance between Dallas and New York is 1260 miles?
A. 60 m/hr
B. 90 m/hr
C. 120 m/hr
D. 135 m/hr
E. 180 m/hr
Relative speed of train A and train B is 90-60=30 miles per hour, thus B will gain 30 miles every hour compared to A.
Now, in 3 hours (from 6 P.M. to 9 P.M.) that A traveled alone, it covered 60*3=180 miles. To catch up A (to meet A), B will need 180/30=6 hours.
Next, in 6 hours B will cover 6*90=540 miles to the meeting point, thus C covered 1260-540=720 miles.
Since C also needed 6 hours to meet A and B (C also left at 9 P.M), then its rate is 720/6=120 miles per hour.
Answer: C.
Hope it's clear.
Can you please explain : To catch up A (to meet A), B will need 180/30=6 hours
Hi
Anu26,
The question uses the concept of relative speed. Let me explain it you its working.
Refer the following diagram for this question:
The diagram shows the relative positioning of trains at 9 PM. Trains B & C are starting from NY & Dallas respectively while train A is at a distance of 180 miles from NY ( as train A started from NY at a speed of 60 miles/hr 3 hours before at 6 PM. SO distance traveled by train A = 60 * 3 = 180 miles)
Since all the trains meet at the same point, it would be enough if we found out meeting point of trains A & B. Train A is 180 miles ahead of train B at 9 PM and the difference between the speeds of trains A & B is 30 miles/hr (Train B travels at a speed of 90 miles/hr and train A travels at a speed of 60 miles/hr).
Using the formula for
Distance = Speed * Time, we can say that 180 = 30 * t i.e. t= 6 hours. This means that train B and A will meet 6 hours after 9 PM. In other words, train B will catch up with train A after 6 hours.
So, distance travelled by train B in 6 hours = 90 * 6 = 540 miles. Thus train C will need to travel 1260 - 540 = 720 miles in 6 hours. So, speed of train C would be \(\frac{720}{6} = 120\) miles/hour
In Distance & Speed question which involves concept of relative speed, it is always helpful to draw a diagram and visualize the solution.
Hope its clear!
Regards
Harsh