A man and a woman agree to meet at a cafe about noon. If the man arrives at a time uniformly distributed between 11:30 and 12:10 and if the woman independently arrives at a time uniformly distributed between 11:50 and 12:35, what is the probability that the first to arrive waits no longer than 15 minutes?

5/21

Step-by-step explanation:

From the question and time interval given the Man will most likely arrive before the woman so i will breakdown the various possible arrival time of the Man in relation to the woman's arrival time.

lets say

11:40 to 11:50

probability of arrival by the man = 10/35

during this period the woman has a probability of arriving less than 10 minutes within a 5 minutes interval

her own probability = 5/60

11:50 to 12:00

probability of arrival by the man = 10/35

during this period the woman has a probability of arriving within 10 minutes of the man's arrival within a 15 minute interval

her probability of arrival = 15/60

12:00 to 12:15

probability of arrival by the man = 15/35

during this period the woman has a probability of arriving within 20 minutes interval

her probability = 20/60

therefore to get the probability that the first to arrives waits no longer than 15 minutes

we multiply the various probabilities for each time interval and then add them up

= ( 10/35 * 5/60 ) + ( 10/35 * 15/60 ) + ( 15/35 * 20/60 )

= 500/2100

= 5/21

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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