Running at 5/4 of his usual speed, an athlete improves his timing by 5 minutes. The time he usually takes to run the same distance is?
A. 30 min
B. 28 min
C. 25 min
D. 30 min
E. None of these
#Approach 1:
In both cases , the distance traveled is constant and we Distance = Speed * Time .
Let the usual speed be S and time taken is T hours.
The new speed =\(\frac{ 5}{4}\) S and new time taken = T - \(\frac{5}{60}\) as he reduces the time by 5 min.( 5 min = 5/60 hours)
Since distance covered is same in both cases, we can equate both.
Distance = Speed * Time .
S*T =\(\frac{ 5}{4}S*(T-\frac{5}{60})\)
T =\(\frac{5}{4}\)*(T-\(\frac{5}{60}\))
4T = 5T - 5*\(\frac{5}{60}\)
T = \(\frac{25}{60}\) hours = 25 mins
Option C is the answer.#Approach 2:
When the Distance covered is constant, the speed and time are inversely proportional.
For Example: If you double your speed, the time taken to cover the same distance would be halved.
We can apply the same property of Speed and Time here as well as the distance covered is the same.
Here the speed of the person is increased from S to 5/4 S , that means his time taken should decrease from T to 4/5T.
If the normal time taken by him is T mins, then the new time taken = \(\frac{4}{5}\)T mins
We know that he improves his timing by 5 mins,i.e T -\(\frac{ 4}{5}\)T = 5 mins
Solving the equation,
T/5 = 5
T= 25 mins.
Option C is the answer.Thanks,
Clifin J Francis,
GMAT SME _________________