Lewis and Geraint left Acaster to travel to Beetown at the same time. Lewis stopped for an hour in Beetown and then drove back towards Acaster. He drove at a constant 70 km/h 70 km/h . He met Geraint, who was cycling at a constant 30 km/h 30 km/h , 105 km 105 km from Beetown. How far is it from Acaster to Beetown?
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Step-by-step explanation:
As both the bus and cyclist are moving in the same direction their relative velocity will be −
Relative velocity of bus =V
B
−V
C
=V
B
- (+20)
Distance covered =V
T
Speed×Time=Distance
(V
B
−20)×18=V
BT
... ... ... ... (1)
Case 2 − Bus moving from B to A
As the bus and cyclist are moving in the opposite direction their relative velocity will be −
Relative velocity of bus =V
B
−V
C
=V
B
-(-20)
Distance covered =V
T
Speed×Time=Distance
V
B
+20)×6=V
BT
... ... ... ... (2)
Solving equations (1) and (2) −
(V
B
−20)×18
V
B
=40km/hr
Substituting value of V
B
in equation (2) −
(40+20)×6=40T
T=9minutes
Speed of the bus is 40km/h and time interval after which each bus leaves is 9 minutes.
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