Answer:
The answer should be 15
Step-by-step explanation:
Let the speed of bus for the exact time = x km/h
the distance between the cities = y km
then the exact time would be, t hours = (y/x) hours
<span> If the bus goes at the rate of 50km/h, then it will arrive B 42min later,
speed = 50 km/h
42 minutes = 42/60 hours = 7/10 hours = 0.7 hours
time taken = t+0.7
distance = speed</span>×time
⇒ y = 50×(t+0.7)
⇒ y = 50t + 35 ---------------------(1)
it increases its speed 5.5/9 m/sec,<span> it will arrive B 30min earlier.</span>
5.5/9 m/s = (5.5/9)×(18/5) km/h = 2.2 km/h
30 minutes = 30/60 = 0.5 hour
speed = (x+2.2) km/h
time = (t - 0.5) hours
distance = speed×time
⇒ y = (x+2.2)×(t-0.5)
⇒ y = ((y/t) +2.2)×(t-0.5) (t = y/x)
⇒ y = y - 0.5 (y/t) + 2.2t - 1.1
⇒ 0.5 (y/t) - 2.2t + 1.1 = 0 (subtracting y from both sides)
⇒ (y/t) - 4.4t - 2.2 = 0 (dividing both sides by 0.5)
⇒ y - 4.4t² - 2.2t = 0 (multiplying both sides by t)
⇒ 50t + 35 - 4.4t² - 2.2 t = 0 (from equation 1)
⇒ -4.4t² + 35 + 47.8t = 0
⇒ 4.4t² - 47.8t - 35 = 0
solving the quadratic equation, we get t = 11.55 hours
y = 50t + 35 = 612.5 km
x = 612.5/11.55 = 53 km/h
A) 612.5 km
B) 11.55 hours
C) 53 km/h
Answer:
6/7
In decimal form it would be 0.85714285714