Uniform Motion Related Problem
Jessie has a 15 km head start on Melvin. How long will it take Melvin to catch Jessie if the latter travels at 70 kph and the former at 100 kph?
Melvin travels 30 km/hr faster than Jessie.
So, how long does it take to cover extra 15 km?
To solve this uniform motion problem, we can use the formula:
Time = Distance / Speed
Let's break down the problem:
1. Jessie has a 15 km head start on Melvin.
This means that when Melvin starts, Jessie is already 15 km ahead.
2. Melvin travels at 100 kph.
This implies that Melvin's speed is 100 kilometers per hour.
3. Jessie travels at 70 kph.
This means that Jessie's speed is 70 kilometers per hour.
To determine how long it will take Melvin to catch up to Jessie, we need to find the time it takes for the distances they travel to be equal.
Let's assume it takes Melvin time 't' to catch up to Jessie. During this time, Melvin will cover a distance equal to the head start Jessie had, plus an additional distance.
Given that Melvin's speed is greater than Jessie's speed, we can write the equation:
Distance covered by Melvin = Distance covered by Jessie + Head Start Distance
Let's substitute the distance, speed, and time into the equation:
100t = 70t + 15
Now, we can solve the equation for 't', which represents the time it takes for Melvin to catch up with Jessie.
100t - 70t = 15
30t = 15
t = 15 / 30
t = 0.5 hours
Therefore, it will take Melvin 0.5 hours (or 30 minutes) to catch up to Jessie.