In a 1500 m race, if vehicle P gives vehicle Q a start of 200m, vehicle P wins the race by 8 sec. Alternatively, if vehicle P gives vehicle Q a start of 400 m, the race ends in a dead heat. How long does vehicle P take to run 1500 m ?
Answer & explanation
Correct answer: option 1
Let’s assume speed of P = x and speed of Q = y
Then, in a 1500 m race distance run by P= 1500 m and distance run by Q after getting head start of 200m = 1300m
Time taken by P = \(\frac{1500}{x}\)
Time taken by Q = \(\frac{1300}{y}\)
Since Q lacks behind by 8 sec therefore Time taken by Q is more as compare to that of P by 8 sec,
\(\frac{1300}{y}\) - \(\frac{1500}{x}\) = 8 ----(1)
When Q gets head start of 400m they both finish the race at same time,
Time taken by Q = \(\frac{1500 - 400}{y}\)= \(\frac{1100}{y}\)
Time taken by P = \(\frac{1500}{x}\)
Both finish at same time,
\(\frac{1100}{y}\) = \(\frac{1500}{x}\)
x = \(\frac{15}{11}\) × y ----(2)
Putting (2) in (1) we get,
\(\frac{200}{y}\) = 8
y = 25 m /sec
And x = \(\frac{375}{11}\) m sec
Time taken by P to run 1500 m = \(\frac{1500 × 11 }{375}\)
= 44 sec