Question

A man travels 370km partly by train and partly by bus if he covers 250km by train and rest by bus it takes him 4 hours but if he travels 130km by train and rest by bus he takes 18 minutes longer find the speed of train and that of bus

Answer 1

250/x + 120/y =4
substitue 1/x with a & 1/y with b
250a+120b=4
130/x + 140/y = 4.3
130a+140b=4.3
250 a + 120 b = 4 .............1
130 a + 140 b = 4.3 .............2
Eliminate y
multiply (1)by -7
Multiply (2) by 6
-1750 a -840 b = -28
780 a + 840 b = 25.8

Add the two equations
-970 a = -2.2
/ -970
a = 0.00227
plug value of a in (1)
250 a + 120 b = 4
0.57 + 120 b = 4
120 b = 4 -0.57
120 b = 3.43
b = 0.02861
x=1/a= 1/0.00227= 440 km/h-------------Train
y=1/b=1/0.02861= 35 km/h-------------- Car
CHECK
130/440 +140/35= 4.3 hours

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