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
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
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.
A) Let's assume the average speed of lorry y as "v" km/h. Since lorry x traveled at an average speed of 15 km/h less than y, the average speed of lorry x would be "v - 15" km/h.
To calculate the average speed of lorry y, we can use the formula:
Average Speed = Total Distance / Total Time
Since both lorries traveled 420 km, and lorry x took an extra 1 hour and 24 minutes (which is 1.4 hours), the total time for lorry x would be the same as lorry y plus 1.4 hours.
So, the equation becomes:
v = 420 km / (v + 1.4)
To solve for v, we can multiply both sides by (v + 1.4):
v(v + 1.4) = 420
Expanding the equation:
v² + 1.4v = 420
Rearranging the equation:
v² + 1.4v - 420 = 0
Factoring the quadratic equation:
(v + 21)(v - 20) = 0
Solving for v, we get two possible values:
v = -21 or v = 20
Since the average speed cannot be negative, the average speed of lorry y is 20 km/h.
B) To calculate the distance between lorry x and town A when lorry y reached town B, we need to determine the time it took for lorry y to reach town B.
Since the average speed of lorry y is 20 km/h, and the total distance is 420 km, we can use the formula:
Time = Distance / Speed
The time it took for lorry y to reach town B is:
Time = 420 km / 20 km/h = 21 hours
Now, since lorry x traveled 1 hour and 24 minutes longer, the total time for lorry x would be:
Total Time for lorry x = 21 hours + 1.4 hours = 22.4 hours
To calculate the distance of lorry x from town A, we multiply its average speed by the total time:
Distance = Speed x Time
Distance = (v - 15) km/h x 22.4 hours
Since we know v = 20 km/h, we can calculate the distance:
Distance = (20 - 15) km/h x 22.4 hours
Distance = 5 km/h x 22.4 hours
Distance = 112 km
Therefore, lorry x was 112 km away from town A when lorry y reached town B.
C) To calculate how far from town A the van met lorry y, we need to determine the time it took for lorry y to leave town A.
Since we know lorry y took 21 hours to reach town B, the van also left town B at the same time as lorry y. The average speed of the van is 90 km/h.
To calculate the distance the van traveled, we use the formula:
Distance = Speed x Time
Distance = 90 km/h x 21 hours
Distance = 1890 km
Therefore, the van met lorry y 1890 km from town A.