1) The distance between two stations is 300 km. Two motorcyclists start simultaneously from these stations and move towards each other. The speed of one of them is 7 km/h more than that of the other. If the distance between them after 2 hours of their start is 34 km. find the speed of each motorcyclist.
2) The difference between the ages of two cousins is 10 years. 15 years ago, if the elder one was twice as old as the younger one, find their present ages.
2) The difference between the ages of two cousins is 10 years. 15 years ago, if the elder one was twice as old as the younger one, find their present ages.
Answers & Comments
Answer-1- 34km
Answer-2-25years
Step-by-step explanation:
1 - The distance between two stations = 300 km
Let the speed of first motorcyclists = x km/h
and speed of second motorcyclists = (x + 7) km/h
Distance covered by the first = 2x km
and distance covered by the second = 2 (x + 7) km = 2x + 14 km
∴
Distance uncovered by them = 300 - (2x + 2x + 14) kms.
According to the condition,
300 - (4x + 14) = 34
⇒
300 - 4x - 14 = 34
⇒
300 - 14 - 34 = 4x
⇒
4x = 300 - 48
⇒
4x = 252
⇒
x
=
252
4
=
63
∴
Speed of the first motorcyclists = 63 km/h
and speed of second = 63 + 7 = 70 km/h
Check. Distance covered by both of them
= 2
×
63 + 2
×
70 = 126 + 140 = 266
Total distance = 300 km.
∴
Distance between them = 300 - 266 = 34 km.
2 -- Let age of elder cousin = x years
and age of younger = (x - 10) years.
15 years ago,
age of older, cousin = x - 15 years
and age of younger = x - 10 - 15
= (x - 25) years.
According to the condition,
x - 15 = 2 (x - 25)
⇒
x - 15 = 2x - 50
⇒
2x - x = 50 - 15
⇒
x = 35
∴
Age of elder cousin = 35 years
and age of younger = 35 - 10
= 25 years Ans.
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