Towns a and b are 420km apart two lorries departed from a at the same time traveling towards b lorry x travelled at an average speed of 15 km/h less than y and reached 1 hour and 24 minutes later

Question

A) calculate the average speed of lorry y
B)how far was x from a when y reached b
C)a van left town b heading towards a in the time 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

Let's assign variables to the unknown values:
Let the speed of lorry Y be "s".
The speed of lorry X will be "s - 15" km/h.

A) To calculate the average speed of lorry Y, we need to find the time it took for lorry Y to reach town B. Since we know the distance between the two towns is 420 km, and the time difference between lorry X and lorry Y is 1 hour and 24 minutes (or 1.4 hours), we can set up the following equation:

420 = (s)(t)
420 = (s)(t + 1.4)

Since the distance for both lorries is the same, we can set these two equations equal to each other and solve for t:

s(t) = (s - 15)(t + 1.4)

Now, we can solve for t:

st = st + 1.4s - 15t - 21

Rearranging the equation:

1.4s = 15t + 21

Dividing both sides by 1.4:

s = (15t + 21)/1.4

We know that t is the time it took for lorry Y to reach town B. Since we are looking for the average speed of lorry Y, we need to find the distance divided by time:

s = 420/t

Setting the two equations equal to each other:

420/t = (15t + 21)/1.4

Cross-multiplying and simplifying:

420 * 1.4 = 15t + 21t
588 = 36t
t ≈ 16.33 hours

Now, we can substitute this value of t back into the equation for the average speed of lorry Y:

s = 420/t
s = 420/16.33
s ≈ 25.71 km/h

Therefore, the average speed of lorry Y is approximately 25.71 km/h.

B) To find how far lorry X was from town A when lorry Y reached town B, we need to calculate the distance traveled by lorry X in the time it took for lorry Y to reach town B. Since we know lorry X traveled for 1 hour and 24 minutes longer than lorry Y, we can set up the following equation:

dX = (s - 15)(t + 1.4)

Substituting the values we found earlier:

dX = (25.71 - 15)(16.33 + 1.4)
dX ≈ 155.03 km

Therefore, lorry X was approximately 155.03 km from town A when lorry Y reached town B.

C) To find how far from town A the van met lorry Y, we need to calculate the distance traveled by the van in the same time that lorry Y traveled. We know that the van traveled at an average speed of 90 km/h, and the time it took for lorry Y to reach town B is t, which we found to be approximately 16.33 hours.

Therefore, the distance traveled by the van is:

dVan = 90 * 16.33
dVan ≈ 1469.7 km

Therefore, the van met lorry Y approximately 1469.7 km from town A.