Two friends decide to cycle to a picnic spot the first person cycles 5 and a 1/2 km/hour and 2nd cycles 6 and a3/4 km/hour to make up for being slow the first person starts out two and half hour earlier after how much time and distance will the 2nd person catch up with the first ??

Question

Two friends decide to cycle to a picnic spot the first person cycles 5 and a 1/2 km/hour and 2nd cycles 6 and a3/4 km/hour to make up for being slow the first person starts out two and half hour earlier after how much time and distance will the 2nd person catch up with the first ??

Answer 1

so, what have you come up with so far?

Answer 2

To find out when the second person catches up with the first person, we need to determine the time it takes for both of them to cover the same distance.

Let's first find the relative speed of the second person compared to the first person:
Relative Speed = Speed of the second person - Speed of the first person

The speed of the first person is 5 and a 1/2 km/hour, which can be written as 11/2 km/hour.
The speed of the second person is 6 and 3/4 km/hour, which can be written as 27/4 km/hour.

Relative Speed = 27/4 - 11/2 = 27/4 - 22/4 = 5/4 km/hour

Now, since the first person starts 2 and a half hours earlier, we need to account for that time difference.
Distance traveled by the first person = Speed of the first person * Time taken by the second person

Let's assume the time taken by the second person to catch up is T hours.

Distance traveled by the first person = (11/2) * T

Distance traveled by the second person = (27/4) * (T + 2.5) (adding 2.5 hours due to the time difference)

Since the second person catches up with the first person, their distances will be equal.

(11/2) * T = (27/4) * (T + 2.5)

To solve for T, we can cross multiply:

(11/2) * T = (27/4) * (T + 2.5)
(11/2) * T = (27/4) * T + (27/4) * 2.5
(11/2) * T = (27/4) * T + 27/2
11T = 27T/2 + 27 * 2
11T = 27T/2 + 54
Multiplying both sides of the equation by 2 to get rid of the fraction:
22T = 27T + 108
27T - 22T = 108
5T = 108
T = 108/5
T = 21.6

Therefore, the second person catches up with the first person after 21.6 hours.

To find the distance covered at this time, we can substitute T into either the distance formula for the first person or the second person.

Distance traveled by the first person = (11/2) * 21.6
= 118.8 km

Therefore, the second person catches up with the first person after 21.6 hours, and the distance covered at that time is approximately 118.8 km.

Two friends decide to cycle to a picnic spot the first person cycles 5 and a 1/2 km/hour and 2nd cycles 6 and a3/4 km/hour to make up for being slow the first person starts out two and half hour earlier after how much time and distance will the 2nd person catch up with the first ??

so, what have you come up with so far?

answer me

To find out when the second person catches up with the first person, we need to determine the time it takes for both of them to cover the same distance.