Abdul travelled 300 km by train …
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Gaurav Seth 4 years, 8 months ago
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
----------------------------------------------------------------------------------
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)
-------------------------------------------------------------------------
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)
-------------------------------------------------------------
Solving equations 1 and 2,
260a + 240b = 5.6 ---------> multiply by 5
300 a + 200 b =5.5 ---------> multiply by 6
========================
1300 a + 1200b = 28
1800a + 1200b = 33
----------------------------------
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
-----------------------------------------------
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
0Thank You