Question

Abdul travelled 300 km by train and 200 km by taxi taking 5 hours 30 minutes. But if he travels 260 km by train and 240 km by taxi he takes 6 minutes longer. Find the speed of the train and that of the taxi.

Answer 1

let the speed of train be xkm/hr and taxi be y km/hr

speed = distance / time
time = distance / speed

=> 300/x+ 200/y = 5.5 (30 minutes = 0.5 hr).........(1)



=> 260/x+ 240/ y= 5 hr+ 30 min + 6
=> 260/x + 240/y = 300min + 36 min
=> 260/x + 240/y = 336 min
=> 260/x + 240/y = 5.6 hr .... 336min = 336/60 hr)

=>260/x + 240/y = 5.6 hr...(2)

let 1/x be a and 1/y be b

=> 300/x+ 200/y = 5.5
=> 300a+ 200b= 5.5
(multiplying by 10).... [to remove decimal]

=>3000a+ 2000b=55......(3)
=>600a+ 400b= 11.....(4).....dividing by 5



=>260/x + 240/y = 5.6
=>260a+240b=5.6

(multiplying by 10).... [to remove decimal]

=>2600a+2400b=56....(5)
=>1300a+ 1200b=28....dividing by 2

=>650a+600b=14...(6)

multiplying (4) by 6 and (6) by 4


6(600a+ 400b= 11)....(4)
3600a+2400b=66....(7)

4(650a+600b=14).....(6)

2600a+2400b=56.......(8)

subtracting (7) and (8)

3600a+2400b=66....(7)
2600a+2400b=56.......(8)
-.............-.............-.....
100a=10
a=1/10

hence 1/x=a
1/x=1/10
x=10 km/hr

hope this helps

do let me know if there are any mistakes....:-)