Question

Buses ply from city A to city B at regular interval of 15 minutes. Every bus from A to B moves with constan speed 40 km/h. A car X moving from city B to city A meets buses at an interval of 5 minutes. The speed the car X is n × 10 km/h. Find the value of n.​

Answer 1

The value of n is 8

GIVEN

Buses ply from city A to city B at regular interval of 15 minutes. Every bus from A to B moves with constant speed 40 km/h. A car X moving from city B to city A meets buses at an interval of 5 minutes. The speed the car X is n × 10 km/h.

TO FIND

The value of n

SOLUTION

We can simply solve the above problem as follows;

Speed of every bus, V₁ = 40 km/hr

It is given that,

Each bus ply after 15 minutes (15/60 hour)

Distance travelled by each bus in 15 minutes = 40 × (15/60) = 10 km

Distance travelled by Car X = B to A

Speed of the Car X, = V₂

It is given that the each bus meets the car in 5/60 hour interval.

Distance travelled by bus in 5 minutes = 40 × 5/60 = 10/3 km

Distance travelled by car in 5 minutes = V₂ ×5/60 km

Now,

Total distance = Distance travelled by bus in 5 minutes + Distance travelled by car in 5 minutes

$10 = \frac{V₂}{12} + \frac{10}{3}$

$10 = \frac{V₂ + 40}{12}$

120 = V₂ + 40

V₂ = 120-40 = 80km/hr

V₂ = 80km/hr

Given,

Value of V₂ = n × 10

Comparing The value of V₂

n × 10 = 80

n = 8

Hence, The value of n is 8

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Answer 2

Answer:         n is 8

Explanation:

The aforesaid issue is easily resolved by doing the following:

Every bus travels at a $40 km/hr$ speed.

Considering that,

Every bus runs once every 15 minutes (15/60 hours).

Each bus travels 10 kilometers in 15 minutes, or 40 kilometers in 15 minutes.

The distance driven by Car X is from B to A.

Car's top speed X, equals V2.

Each bus meets the car at intervals of 5/60 hours, as is the case.

Bus travel distance in 5 minutes is equal to $40 * 5/60, (or) 10/3 km$.

$V_{2} = 5/60$ of the distance driven in an automobile in five minutes.

Now,

Total distance equals the sum of the five-minute bus ride and the five-minute drive.

$10=\frac{V{2}}{12}+\frac{10}{3}$

$10=\frac{V_{2}+40}{12}$

$120 = V_{2} + 40V_{2} = 120-40 = 80km/hrV_{2} = 80km/hr$

Given,

V2 value equals n 10

Comparison of V2 Value

$n * 10 = 80n = 8$

Hence, The value of n is 8

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