The total distance between warehouse M and warehouse N is 900 km. Courier Y and Courier Z can travel the entire route between M and N in ‘X’ hours and (X + 4) hours respectively. If Courier Z and Courier Y begin their journeys from warehouse M at 6.00 am and 8.00 am respectively and both couriers cross paths at 10.30 am, what is the distance between warehouse M and the location where they meet?

Correct Answer: 450 km

Step-by-step Explanation:

Step 1: Understand the given data

Total distance between Warehouse M and Warehouse N = 900 km.

Time taken by Courier Y to cover 900 km = X hours.

Time taken by Courier Z to cover 900 km = (X + 4) hours.

Courier Z starts from M at 6:00 am.

Courier Y starts from M at 8:00 am.

They cross paths (meet) at 10:30 am.

Step 2: Calculate the travel time for each courier until they meet

From 6:00 am to 10:30 am, the time duration for Courier Z is 4.5 hours or

$\frac{9}{2}$

hours.

From 8:00 am to 10:30 am, the time duration for Courier Y is 2.5 hours or

$\frac{5}{2}$

hours.

Step 3: Express their speeds in terms of X

Speed of Courier Y,

$S_Y=\frac{900}{X}$

km/h.

Speed of Courier Z,

$S_Z=\frac{900}{X+4}$

km/h.

Step 4: Equate the distance traveled by both couriers from Warehouse M

Since both couriers start from Warehouse M and meet at the same location, the distance covered by Courier Z in 4.5 hours is equal to the distance covered by Courier Y in 2.5 hours.

Distance = Speed × Time

$S_Z\times 4.5=S_Y\times 2.5$

Substitute the expressions for speed:

$\frac{900}{X+4}\times 4.5=\frac{900}{X}\times 2.5$

Divide both sides by 900:

$\frac{4.5}{X+4}=\frac{2.5}{X}$

Cross-multiply to solve for X:

$4.5X=2.5(X+4)$

$4.5X=2.5X+10$

$2X=10$

$X=5$

Step 5: Calculate the distance from Warehouse M to the meeting location

Now, calculate the speed of Courier Y:

$S_Y=\frac{900}{5}=180$

km/h.

Distance covered by Courier Y in 2.5 hours:

$\text{Distance}=180\times 2.5=450$

km.

Therefore, the distance between warehouse M and the meeting location is 450 km.