Question

Kali left school and traveled toward her friend's house at an average speed of 40 km/h. Matt left one hour later and traveled in the opposite direction with an average speed of 50 km/h. Find the number of hours Matt needs to travel before they are 400 km apart.

Answer 1

Step-by-step explanation:

At the time when they are 400 meters apart, the total distance that Kali and matt would have covered is 400 meters.

Kali left school and traveled toward her friend's house at an average speed of 40 km/h. Let t represent the time it took Kali to travel before they are 400 meters apart.

Distance = speed × time

Therefore, distance covered by Kali would be 40 × t = 40t

Matt left one hour later and traveled in the opposite direction with an average speed of 50 km/h. The time that Matt spent travelling would be t - 1. Therefore, distance travelled by Matt would be 50(t - 1)

Since the sum of their distances is 400 km, then,

40t + 50t - 50 = 400

90t - 50 = 400

90t = 450

t = 450/90 = 5

the number of hours Matt needs to travel before they are 400 km apart would be

t - 1 = 5 - 1 = 4 hours

Answer 2

t = 5 hr

Step-by-step explanation:

Let kali moves toward east with velocity= V₁= 40 km/ h

Mat moves toward west with velocity = V₂= 50 km/hr

As Klai left one hour earlier = t₁= 1 hr

distance traveled in 1st hour = s₁ = v * t = 40 * 1 = 40 km

Remaining distance = 400 - 40 = 360 km

As they move in the opposite directions:

Relative speed= 40 + 50 = 90 km/ h

s = v * t

⇒ t = s / v

⇒ t₂ = 360 / 90

⇒ t₂ = 4 hr

Total time = t = t₁ + t₂

t = 1 hr + 4 hr

t = 5 hr