Places M and N are 90 km apart from each other on a national highway. A truck starts from M and another from N at the same time. If they go in the same direction, then they meet in 9 hours and if they go in opposite directions they meet in 9/7hours. The speed of the trucks are _______.a)90 km/hr, 40 km/hrb)40 km/hr, 30 km/hrc)20 km/hr, 60 km/hrd)50 km/hr, 12 km/hrCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Let x km/hr be the speed of truck starting from M and y km/hr be the speed of truck starting from N.
Case I : If they meet at P.

⇒ 10 + y = x ...(1)
Case II : If they meet at P.

For M,

⇒ 70 = x + y ...(2)
Solving (1) and (2), we get
y = 30 km/hr and x = 40 km/hr

Answer

Given:
Distance between M and N = 90 km

When the trucks go in the same direction:
Time taken to meet = 9 hours

When the trucks go in opposite directions:
Time taken to meet = 9/7 hours

Let the speed of one truck be x km/hr and the speed of the other truck be y km/hr.

When the trucks go in the same direction:
Relative speed = (x - y) km/hr
Distance traveled = 90 km
Time taken = 9 hours

Using the formula:
Distance = Speed × Time
90 = (x - y) × 9

Simplifying the equation:
10 = x - y ...........(1)

When the trucks go in opposite directions:
Relative speed = (x + y) km/hr
Distance traveled = 90 km
Time taken = 9/7 hours

Using the formula:
Distance = Speed × Time
90 = (x + y) × (9/7)

Simplifying the equation:
10 = (x + y) × (1/7) ...........(2)

Solving equations (1) and (2) simultaneously:
x - y = 10
x + y = 70/7

Adding the two equations:
2x = 10 + 70/7
2x = (70 + 10/7)
2x = 80/7

Dividing by 2 on both sides:
x = (80/7) ÷ 2
x = 40/7

Substituting the value of x in equation (1):
40/7 - y = 10

Simplifying the equation:
y = 40/7 - 70/7
y = -30/7

Since speed cannot be negative, we take the positive value:
y = 30/7

Therefore, the speed of the trucks are:
Truck 1: x = 40/7 km/hr
Truck 2: y = 30/7 km/hr

So, the correct answer is option (b) 40 km/hr and 30 km/hr.

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