A man travels a certain distance at his usual speed. If he reduces his speed by 5 miles per hour, he reaches 5 hours late. if he increases his speed by 15 miles per hour. he reaches 7.5 hours early. How much distance has to be traveled?
A. 1000 miles
B. 500 miles
C. 1500 miles
D. 750 miles
Answers
Solution :-
Let us assume that, initial speed of man is S miles / h and actual time taken by him is T hours.
so,
→ Actual speed * Late time = Reduced speed * (T + Late time)
→ S * 5 = 5(T + 5)
→ 5S = 5T + 5
→ 5S - 5T = 5
→ S - T = 1 ------ Eqn.(1)
and,
→ Actual speed * Early time = Increased speed * (T - Early time)
→ S * 7.5 = 15(T - 7.5)
→ 7.5S = 15T - 112.5
→ 7.5S - 15T = -112.5
→ S - 2T = -15 ------ Eqn.(2)
Subtracting Eqn.(1) from Eqn.(2) ,
→ (S - 2T) - (S - T) = -15 - 1
→ S - S - 2T + T = (-16)
→ (-T) = (-16)
→ T = 16 hours.
putting value of T in Eqn.(1) ,
→ S - 16 = 1
→ S = 17 km/h .
therefore,
→ The distance traveled by him = 16 * 17 = 272 km (Ans.)
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