A takes 2 hours more than B to walk P km, but if A doubles his speed, then he can make it in one hour less than B. How much time does B require for walking P km?
4 hours
Let B take t hours to walk P km. A is slower, taking 2 hours more, so A normally takes (t + 2) hours.
Key idea: for a fixed distance, time is inversely proportional to speed. So if A doubles his speed, his time is halved, becoming (t + 2)/2 hours.
The problem says with doubled speed A finishes one hour less than B, i.e. in (t − 1) hours.
So: (t + 2)/2 = t − 1
Multiply both sides by 2: t + 2 = 2t − 2
Solve: 2 + 2 = 2t − t, so t = 4.
Check: A normally takes 6 h; doubled speed makes it 3 h, which is indeed 1 h less than B's 4 h. Correct.
So B needs 4 hours. The value 3 hours is A's doubled-speed time, not B's; 5 hours and 3.5 hours do not satisfy the halving-and-one-hour-less condition.
Similar Questions
A bus takes two hours less for a journey of 300 km, if its speed is increased by 5 km/hr from its normal speed. The normal speed is.
Important Questions from Speed Time and Distance
A journey of 900 km is completed in 11 h. If two-fifth of the journey is completed at the speed of 60 km/h, at what speed (in km/h) is the remaining journey completed?
A car starts from point A towards point B, travelling at the speed of 20 km/h. 1 \(\frac{1}{2}\) hours later, another car starts from point A and travelling at the speed of 30 km/h and reaches 2 \(\frac{1}{2}\) hours before the first car. Find the distance between A and B.
A bus covered a distance of 162 km. If speed of this bus is 15 m/s, then what will be the time taken ?
An athlete runs an 800 m race in 96 seconds. His speed (in km / h) is:
A person has to cover a distance of 150 km in 15 hours. If he traveled with the speed of 11.8 km/hr for 10 hours. At what speed he has to travel to cover the remaining distance in the remaining time?
