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Question 949647: A train running between City A and City B arrives at its destination 10minutes late when it goes at 40kms.per hour. And 16minutes late when it goes at 30kms. per hour. What is the distance between two cities?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you either want to convert minutes to hours or hours to minutes.
we'll try converting minutes to hours.
you could just as easily solve the problem by converting hours to minutes.
the key is that you need to be dealing with consistent units in order to solve the problem correctly.
10 minutes = 1/6 of an hour.
16 minutes = 4/15 of an hour.
the general equation to use is r*t = d
r = rate of speed in kilometers per hour.
t = time in hours.
d = distance in kilometers.
you have 2 equations to work with.
40*(t+1/6) = d
30*(t+4/15) = d
if you replace d in the first equation with its equivalent value from the second equation, you will get:
40*(t+1/6) = 30*(t+4/15)
simplify by performing the indicated operations to get:
40*t + 40/6 = 30*t + 120/15
subtract 30*t from both sides of the equation and subtract 40/6 from both sides of the equation to get:
40*t - 30*t= 120/15 - 40/6
the least common denominator on the right looks like it's 30, so we'll convert those fractions to fractions with a denominator of 30.
equation becomes:
40*t - 30*t = 240/30 - 200/30
simplify to get 10*t = 40/30
divide both sides of that equation by 10 and you get:
t = 40/300 = 4/30 = 2/15 hours.
now that you know the value of t, you can use that to solve for the distance.
first equation of 40*(t+1/6) = d becomes 40*(2/15+1/6) = d which becomes 40*(4/30 + 5/30) = d which becomes 40*9/30 = d which becomes 360/30 = d which becomes 36/3 = d which becomes 12 = d.
second equation of 30*(t+4/15) = d becomes 30*(2/15+4/15) = d which becomes 30*(6/15) = d which becomes 180/15 = d which becomes 12 = d.
d = 12 in both equation which confirms the value of d is good since d had to be the same in both equations.
the distance between the 2 cities is 12 kilometers.
that's your solution and you can stop here if you wish.
you can go one step further if you like, but you don't have to.
i'll go the one step further just to show you.
now that you know the distance, you can solve for how fast the train should have been going to be on time.
r*t = d is the general equation to use.
you have t = 2/15 and d = 12.
solve for r to get r = d/t = 12/(2/15) which is equal to 12*(15/2) which is equal to 6*15 which is equal to 90 kilometers per hour.
the train needed to be traveling at 90 kilometers per hour to be on time.
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