Question

Pranali and Prasad started walking to the East and to the North respectively, from the same point and at the same speed. After 2 hours distance between them was 15√2 km. Find their speed per hour.

Answer 1

Suppose Pranali and Prasad started walking from point A, and reached points B and C respectively after 2 hours.

Distance between them = BC = 15√2 km

Since, their speed is same, both travel the same distance in the given time. 

∴ AB = AC 

Let AB = AC = x km (i) 

Now, in ∆ ABC, ∠A = 90° 

∴ BC² = AB² + AC² [Pythagoras theorem] 

∴ (15√2)² = x² + x² [From (i)] 

∴ 225 × 2 = 2x² 

∴ x² = 225

∴ x = √225 [Taking square root of both sides] 

∴ x = 15 km 

∴ AB = AC = 15km 

Now, speed = distance/time = 15/2

= 7.5 km/hr 

∴ The speed of Pranali and Prasad is 7.5 km/hour