A man travels some distance at a speed of 12km/hr and returned at 9km/hr.  If the total time taken by the man is 2hrs and 20minutes.  Find the distance

Asked by surajsugitha | 12th Nov, 2015, 07:39: PM

Expert Answer:

Given:
Speed of upward journey = 12 km/hr
Speed for downward (return) journey = 9 km/hr

Total time, t = 2 hr 20 min = begin mathsize 14px style 2 plus 20 over 60 hr equals 2 plus 1 third equals fraction numerator 6 plus 1 over denominator 3 end fraction equals 7 over 3 hr end style
Let the distance travelled be 'x' km.
begin mathsize 14px style Speed equals Distance over Time end style
(i) When speed (upward journey)= 12 km/hr
 begin mathsize 14px style Time comma space straight t equals fraction numerator straight x space km over denominator 12 space km divided by hr end fraction space space space space space space space space space space space equals straight x over 12 hr end style
(ii) When speed (return journey) = 9 km/hr
begin mathsize 14px style Time comma space straight t equals fraction numerator straight x space km over denominator 9 space km divided by hr end fraction space space space space space space space space space space space equals straight x over 9 hr end style
Therefore, total time taken to complete the journey,
begin mathsize 14px style straight x over 12 plus straight x over 9 equals 7 over 3 Multiplying space both space the space sides space by space 3 comma space we space get comma fraction numerator 3 straight x over denominator 12 end fraction plus fraction numerator 3 straight x over denominator 9 end fraction equals 7 over 3 cross times 3 straight x over 4 plus straight x over 3 equals 7 fraction numerator 3 straight x plus 4 straight x over denominator 12 end fraction equals 7 3 straight x plus 4 straight x equals 7 cross times 12 3 straight x plus 4 straight x equals 84 7 straight x equals 84 straight x equals 84 over 7 therefore straight x equals 12 space km end style

Hence, the distance travelled is 12 km.

Answered by Faiza Lambe | 13th Nov, 2015, 11:28: AM