In covering a distance of 30 km, Ali takes 2 hours more than Raza. If Ali doubles his speed, then he would take 1 hour less than Raza. What is the speed of Ali?
- 10 kmph
- 6 kmph
- 5 kmph
- 7.5 kmph
Explanation
1. Let Ali's speed be x kmph. Then, the time taken by Ali to cover 30 km is 30/x hours.
2. Since Ali takes 2 hours more than Raza, the time taken by Raza to cover 30 km is (30/x) - 2 hours.
3. If Ali doubles his speed, his new speed is 2x kmph. The time taken by Ali to cover 30 km at this new speed is 30/(2x) hours.
4. According to the problem, if Ali doubles his speed, he would take 1 hour less than Raza. So, we can set up the equation:
(30/x) - 2 = (30/(2x)) - 1
Simplifying the equation, we get:
30/x - 2 = 15/x - 1
Multiplying both sides by x, we get:
30 - 2x = 15 - x
Simplifying further, we get:
x = 5
So, Ali's speed is 5 kmph.
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