The sabarmati express left ahmedabad for mumbai. having travelled 300 km, which constitutes 200/3 percent of the distance between ahmedabad and mumbai, the train was stopped by a red signal. half an hour later, the track was cleared and the engine driver, having increased the speed by 15 km per hour, arrived at mumbai on time. find the initial speed of the sabarmati express.
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9
The distance covered before the train is stopped is :
200/3 × 1/100 × 300 = 200
Let the initial speed = x km/h
The time taken is :
200 / x
If the train had not been stopped :
Time would be = 300/x
The time remaining to cover the remaining distance is :
300/x - 200/x = 100 / x
After the train had been stopped for 1/2 hr, the new speed is (x + 15) km/h
The time is 100 / (x + 15)
This time is less by 1/2hrs from
100 / x
Meaning :
(100/x) - 1/2 = 100/(x+15)
(x + 15)100×2 - (x + 15)x = 100 × 2 × x
200x + 3000 - x² - 15x = 200x
200x - 200x - x² - 15x + 3000 = 0
x² + 15x - 3000 = 0
Using quadratic formula.
x ={ - 15 +/-√(225 + 12000)} / 2
x = (110.6 - 15) / 2
x = 47.8km/h
200/3 × 1/100 × 300 = 200
Let the initial speed = x km/h
The time taken is :
200 / x
If the train had not been stopped :
Time would be = 300/x
The time remaining to cover the remaining distance is :
300/x - 200/x = 100 / x
After the train had been stopped for 1/2 hr, the new speed is (x + 15) km/h
The time is 100 / (x + 15)
This time is less by 1/2hrs from
100 / x
Meaning :
(100/x) - 1/2 = 100/(x+15)
(x + 15)100×2 - (x + 15)x = 100 × 2 × x
200x + 3000 - x² - 15x = 200x
200x - 200x - x² - 15x + 3000 = 0
x² + 15x - 3000 = 0
Using quadratic formula.
x ={ - 15 +/-√(225 + 12000)} / 2
x = (110.6 - 15) / 2
x = 47.8km/h
Answered by
6
Answer:
ans is 60 kmph ..
Step-by-step explanation:
but its complicated to explain
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