4.Four friends- Sumit, Ajoy ,Parul and Nandini decided to go out for a picnic. If they travel with a speed of 40 km/hr, they reach 30 minutes later than their scheduled time. And if they go with a speed of 60 km/hr, they reach 30 minutes early. They start their journey at 8 a.m. (i) What is their scheduled time to reach the picnic spot?(ii)How far is the picnic spot?(iii) By what speed they have to travel to reach on time?
Answers
Answer:
60 minutes and 100 km
Step-by-step explanation:
30 + 30 = 60
40 + 60 = 100
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Question :
Four friends- Sumit, Ajoy ,Parul and Nandini decided to go out for a picnic. If they travel with a speed of 40 km/hr, they reach 30 minutes later than their scheduled time. And if they go with a speed of 60 km/hr, they reach 30 minutes early. They start their journey at 8 a.m.
(i) What is their scheduled time to reach the picnic spot?(ii)How far is the picnic spot?
(iii) By what speed they have to travel to reach on time?
Answer :
i) The schedule time to reach is 9:30 a.m.
ii) The picnic spot is 120km away.
iii) They have to travel with the speed of 48km/h to reach on time .
Given :
They set out for the journey at 8.a.m
If they travel with a speed of 40 km/hr, they reach 30 minutes later than their scheduled time.
If they go with a speed of 60 km/hr, they reach 30 minutes early.
To find :
The schedule time, the distance of the picnic spot and the speed
Solution :
Let the distance be x km
If they travelled with the speed of 40km/h ,
Time it would take = Distance/ Speed
= x / 40
If they travelled with the speed of 60km/h,
Time it would take = x/60
30mins = 1/2 hours
Hence,
x/40 - 1/2 = x/60 + 1/2
=> x/40 - x/60 = 1/2 + 1/2
=> (3x - 2x)/ 120 = 1
=> x/120 = 1
=> x = 1×120
=> x = 120
Hence, the picnic spot is 120km away.
If they travel at 40km/h speed,
40 = 120 / time+1/2
=> (time + 1/2) × 40 = 120
=> (time + 1/2) = 120/40
=> (time + 1/2) = 3
=> time = 3 - 1/2
=> time = 2.5 hours
Hence, the schedule time to reach is 8a.m + 2.5hours
= 9:30 a.m.
Speed by which they have to travel to reach on time = distance/time
= 120/ 2.5
= 48 km/h
Hence, they have to travel with the speed of 48km/h to reach on time .
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