Towns A and B are 420km apart. Two lorries departed from A at the same time travelling towards B. Lorry x travelled at an average speed of 15km/h less than Y and reached 1 hour 24 minutes later.

Question

c) A van left town B heading towards A at the time lorries x and y left A. If the van travelled at an average speed of 90km/h, how far from A did it meet lorry Y

Answer 1

To find the distance from A where the van met lorry Y, we first need to determine the time it took for lorry Y to reach that point.
Let the average speed of lorry Y be represented by V.
The speed of lorry X is V - 15 km/h.
Let the time it took for lorry Y to reach the meeting point be represented by T hours.

Since distance = speed * time, we have the following equations:

420 = V * T (1)
420 = (V - 15) * (T + 1 2/3) (2)

Let's solve equation (2) to find the values of V and T.

420 = (V - 15) * (1.4T + 1 2/3) [Converting 1 hour 24 minutes to 1.4 hours]
420 = (V - 15) * (7T + 10)/5 [Converting fractions to a common denominator of 5]
5 * 420 = (V - 15) * (7T + 10) [Multiplying both sides by 5]

2100 = (V - 15) * (7T + 10)

Since this equation has two unknowns, V and T, it cannot be solved directly. However, we are given additional information about the van.

The van traveled at an average speed of 90 km/h. Let the time it took for the van to meet lorry Y be represented by T_van hours. The distance traveled by the van is 90 * T_van = D.

From A, the lorries travel a distance of 420 - D before meeting each other. Using equation (1), we can write:

420 - D = V * (T - T_van)

From B, the van travels a distance of 420 - D before meeting lorry Y. Using equation (1), we can write:

420 - D = 90 * (T - T_van)

Setting the two expressions for 420 - D equal to each other, we have:

V * (T - T_van) = 90 * (T - T_van)

Simplifying further:

VT - VT_van = 90T - 90T_van

VT + 90T_van = 90T + VT_van

V(T - T_van) = 90(T - T_van)

Since T - T_van ≠ 0 (because they are different times), we can divide both sides of the equation by (T - T_van):

V = 90

This means that the average speed of lorry Y is 90 km/h.

Now let's go back to equation (1) and substitute V = 90:

420 = 90T

T = 420/90 = 14/3 = 4 2/3 hours

So lorry Y took 4 hours and 40 minutes to reach the meeting point.

Now, let's find the distance from A where lorry Y and the van met. The van traveled at an average speed of 90 km/h for 4 2/3 hours:

D = 90 * (14/3) = 420 km

Therefore, the van met lorry Y 420 km from A.