Abdul travelled 300 km by the train and 200 km by taxi . It took him 5 hours and 30 minutes but if he travelled 260 km by train and 240 km by taxi he takes 6 mins longer . Find the speed of train and that of taxi.
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let speed of train = x km / min
speed of taxi = y km / min
so . according to first condition ,
time taken is ,
300/x + 200/y = 330
30/x + 20/y = 33
20x + 30y = 33xy -------(1)
according to second condition ,
260/x + 240/y = 336
65/x + 60/y = 84
60x + 65y = 84xy -------(2)
eq 1 can be write as
60x + 90y = 99xy -------(3)
subtracting 2 from 3
25y = 15xy
x = 25 /15
x = 5/3 km/min
x = 27.77 meter/second
putting x = 5/3 in above
we get
60x + 65y = 84xy
60 × 5/3 + 65y = 84 × 5/3 × y
100 + 65y = 140y
75y = 100
y = 100/75
y = 5/4 km/min
y = 20.83 meter/second
speed of taxi = y km / min
so . according to first condition ,
time taken is ,
300/x + 200/y = 330
30/x + 20/y = 33
20x + 30y = 33xy -------(1)
according to second condition ,
260/x + 240/y = 336
65/x + 60/y = 84
60x + 65y = 84xy -------(2)
eq 1 can be write as
60x + 90y = 99xy -------(3)
subtracting 2 from 3
25y = 15xy
x = 25 /15
x = 5/3 km/min
x = 27.77 meter/second
putting x = 5/3 in above
we get
60x + 65y = 84xy
60 × 5/3 + 65y = 84 × 5/3 × y
100 + 65y = 140y
75y = 100
y = 100/75
y = 5/4 km/min
y = 20.83 meter/second
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