abdul travels 300km by train and 200km by taxi it takes him 5hrs 30mins . but if he travels 260km by train and 240km by taxi he takes 6mins longer find the speed of the train and the taxi
Answers
Let the speed of train be "x km/hr" and speed of taxi be "y km/hr"
here , distance travelled in both cases is same ,
Total distance = 300 + 200 = 260 + 240 = 500 km
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Case 1 :-
Time taken by train to travel 300 km = distance/speed
= 300/x
Time taken by taxi to travel 200 km = 200/y
so,
300/x + 200/y = 5.5 hour
Let 1/x = a , 1/y = b
300 a + 200 b =5.5 -----> (1)
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Case 2 :-
Time taken by train to travel 260 km = 260/x
Time taken by taxi to travel 240 km = 240/x
It is said , that , it took 6 min more ,
6min = 0.1 hour
time taken = 5.5 + 0.1 = 5.6 hours
so ,
260/x + 240/y = 5.6
260a + 240b = 5.6 ----> (2)
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Solving equations 1 and 2,
260a + 240b = 5.6 ---------> multiply by 5
300 a + 200 b =5.5 ---------> multiply by 6
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1300 a + 1200b = 28
1800a + 1200b = 33
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500a = 5
a = 5/500
= 1/100
260a + 240b = 5.6
260/100 + 240b = 5.6
2.6 + 240b = 5.6
240b = 3
b = 3/240
= 1/80
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we know that
1/a = x , 1/b = y
hence,
x = 100
y = 80
speed of train = 100 km/hr
speed of taxi = 80 km/hr