Question:In a km race, A beats B by 28 metres or 7 seconds. Find A'S time over the course.
Clearly, B covers 28 m in 7 seconds. :.B,s time over the course` = (7/28 xx 1000)` sec = 250 seconds. :. A's time over the course = (250 - 7) sec = 243 sec. = 4 min. 3 sec.
Question:A runs` 1 3/4` times as fast as B. If A gives B a start of 84 m,how far must the winning post be so that A and B might reach it at the same time ?
The ratio of the rates of A and B` = 7/4 : 1 = 7 : 4.` So, in a race of 7 m, A gains 3 m over B. :. 3m are gained by A in a race of 7m. :. 84 m are gained by A in a race of` (7/3 xx 84)` m = 196 m. :. Winning post must be 196 m away from the starting point.
Question:A can run 1 km in 3 min. 10 sec. and B can cover the same distance can A beat B ?
Clearly, A beats B by 10 sec. Distance covered by B in 10 sec.` = (1000/200 xx 10) m` = 50 m. :. A beats B by 50 metres.
Question:In a 100 m race, A runs at 8 km per hour. If A gives B a start of 4 m and still beats him by 15 seconds, what is the speed of B ?
Time taken by A to cover 100 m` = ((60 xx 60)/8000 xx 100) sec.`
= 45 sec.
:. B covers (100 - 4) m = 96 m in (45 + 15) sec
= 60 sec.
:. B's speed` = ((96 xx 60 xx 60)/(60 xx 1000))` km/hr = 5.76 km/hr.Question:A, B and C are three contestants in a km race. If A can give B a start of 40 m and A can give C a start of 64 m, how many metre's start can B give C ?
While A covers 1000 m, B covers (1000 - 40)m = 960 m and C covers (1000 - 64) m or 936 m. When B Covers 960 m, C covers 936 m When B covers 1000 m, C covers` (936/960 xx 1000) m` = 975 m. :. B can give C a start of (1000 - 975) or 25 m.