6. Ramu cycled from his house to school at 10 km/hr and
returned at the rate of 9 km/hr. Babu cycled both ways at
12 km/hr. It was found that for the total journey, Babu took
10 minutes less than Ramu. What is the distance between
school and the house?
Answers
Step-by-step explanation:
10 min = 1/6 hr
avg speed of ramu= 19/2= 9.5
avg speed of babu= 24/2= 6
9.5-6= 1/6 hr
2.5*6= 15 km
Answer:
Distance between school and house is 3.75 km or 3750 m.
Step-by-step explanation:
Let House be point A and School be point B
Now, we are given,
Speed of Ramu from A to B = 10 km/h
Speed of Ramu from B to A = 9 km/h
also,
Speed of Babu from A to B = 12 km/h
Speed of Babu from B to A = 12 km/h
Let the Distance from A to B be 'D' km, since the distance travelled is same from school to house also, from B to A = D km
Speed = Distance/Time
∴ Time = Distance/Speed
Then,
Time taken for Ramu from A to B = D/10
Time taken for Ramu from B to A = D/9
Thus,
Total time taken = (D/10) + (D/9)
= (9D + 10D)/(10 × 9)
= 19D/90 hrs.
also,
Time taken for Babu from A to B = D/12
Time taken for Babu from B to A = D/12
Thus,
Total time taken = (D/12) + (D/12)
= 2D/12
= D/6 hrs.
Now, according to the Question,
Time taken by Babu = Time taken by Ramu - 10min.
Here, time is taken in hours so,
60 min = 1 hr
1 min = 1/60 hrs.
So,
10 min = 10 × (1/60)
= 1/6 hrs.
Hence,
(D/6) = (19D/90) - (1/6)
(19D/90) - (D/6) = 1/6
Taking LCM (6, 90) = 90
(19D/90) - (D/6) × (15/15) = 1/6
(19D/90) - (15D/90) = 1/6
4D/90 = 1/6
Cross multiplying we get,
4D × 6 = 90 × 1
24D = 90
D = 90/24
D = 45/12
D = 15/4
D = 3.75 km
In metres,
1 km = 1000 m
3.75 km = 1000 × 3.75
= 3750 m
Hence,
Distance between school and house is 3.75 km or 3750 m.
Hope it helped and believing you understood it........All the best