A train travels at a particular speed for a duration of one hour, after which one of its engine malfunctions reducing its speed to 3/5th of the actual speed before theoccurrence of fault in engine. It travels at this speed for 2 hours to reach at itsdestination. If the fault had occurred 50 miles later on, the train would have reachedits destination 45 minutes early. Find the distance traveled by the train.

Let the actual speed of train be X miles/hour.
after fault its speed will be reduced to 3X/5 miles/hour.
If we could find the speed of the train, we will get the solution!!!
by seeing one can find that time difference( 45 minutes) occur between two cases,
in the 50 miles distance traveled by the train at two different speeds(X and 3X/5).
=> If the time taken to cover 50 miles at speed 3X/5 is 't' hours then time taken to
travel 50 miles at speed X is t-(45/60) = (t-0.75) hours.
We can write ...=> (3X/5)*t = X*[t-0.75] = 50 miles -->(i)
solving we get... t=15/8 hours.
then substituting value of 't' in first term of eq. (i) => (3X/5)*15/8=50
solving we get... X= 400/9 miles/hour.
Answer : So, solving the problem with first case we get the distance traveled
by the train as 97.77 miles.

Beena
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Sep 15th, 2005
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rahul

Dec 6th, 2005

Let speed be s and distancs be d
for the first case
          1*s +2*3s/5=d
so d/s + d/(3s/5) + 45/60= 50/s +(d-50)/(3s/5)
   substitute value of d from eqn above
   s=498/8
and will be 100 miles
quite an easy way!

Praveen

Jan 12th, 2006

Case first : let us assume speed to train be x miles/hours Total distance travelled in case 1 = x*1 + 3x/5*2 = 11x/5 milesCase 2 : Total distance travelled in case 2 = x+50 + 3x/5*(2-45/60) = 50 +7x/4 comparing these two equations we have x= 1000/9Hence total distance =11x/5 = 11*1000/9 *1/5 = 244.44 miles

Scott McGillivray

Jul 30th, 2006

I get 366.67 miles.
Let v = train full velocity
Let d = distance
Case 1 - train goes (1 hour * v) + (2 hours * 3 v / 5) = d Therefore d = v * 2.2 hours
Case 2 - train covers 50 miles 45 minutes faster at v than at v * 3/5
( 50 miles / (.75 hours) ) = v * 2 / 5 = 0.4 v
v = 166 miles / hourplug v into answer from 1 and you get d = 166 mph * 2.2 hours = 366.67 miles.