In a 100 meter race, if Asha gives Bob a start of 20 meters, then Asha wins the race by 5 seconds. Alternatively, if Asha gives Bob a start of 40 meters the race ends in a dead heat. How long does Asha take to run 200 m?
In a 100 meter race, if Asha gives Bob a start of 20 meters, then Asha wins the race by 5 seconds. Alternatively, if Asha gives Bob a start of 40 meters the race ends in a dead heat. How long does Asha take to run 200 m?
1). 10 seconds
2). 20 seconds
3). 30 seconds
4). 40 seconds
1 answers
Let’s assume speed of Asha as va and speed of Bob as vb
Then, in a 100 M race distance run by Asha= 100 M and distance run by Bob after getting head start of 20 M = 80M
Time taken by Asha = 100/va
Time taken by Bob = 80/vb
Since Bob lacks behind by 5 sec therefore Time taken by Bob is more as compare to that of Asha by 5 sec,
$(\therefore \frac{{80}}{{{v_b}}}\; - \frac{{100}}{{{v_a}}} = 5)$ ----(1)
When Bob gets head start of 40M they both finish the race at same time,
Time taken by Bob = (100-40)/vb = 60/vb
Time taken by Asha = 100/va
Both finish at same time,
∴ 60/vb = 100/va
⇒ va = 5/3 × vb ----(2)
Putting (2) in (1) we get,
Vb = 4 and va = 20/3
Time taken by Asha to complete 200M race would be 200/ va = 30seconds
Thus time taken by Asha would be 30 seconds.Other Questions
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