Really simple math question embaressed I'm asking.

[RIPP_n_WIPE]

Okay. I'm finally getting my feet wet again mathematically. I've been out of the loop for about a year and a half and am surprised about how much I've lost.

So here's the question.

Alice and Bob are going from their home to a friend’s house, traveling by foot. Alice leaves home first and strolls slowly at a rate of 2 mph towards the friend’s house. Twelve minutes later (1/5 hour later), Bob leaves home and jogs towards the friend’s house at 5 mph.

(a) When will Bob catch up to Alice?
(State your final answer carefully as either “Bob will catch up to Alice ___ minutes after Bob leaves home” or “Bob will catch up to Alice ___ minutes after Alice leaves home”)

(b) How far has each person traveled at this point?

I dunno exactly what I'm doing wrong with it. I refuse to guess and check for the answer.

Thus far I've set up the two like my book had a similar question set up. Where Alices distance = d and her rate is 2 and her time being t+1/5 getting me 2t+2/5. Bobs distance = d his rate = 5 and his time t yielding me 5t. When I set up the equality of 5t = 2t+2/5 gets me t=2/15 which I know is off because Alice is already gone for 1/5 of an hour,

[General Soontir Fel]

You solved everything correctly. The equations solve to t=2/15, where t is the time since Bob left the house. So Bob will catch up to Alice 2/15 of an hour, or 8 minutes after leaving the house, which is 20 minutes after Alice left. Since Bob jogs at 5 mph, it will be (2*5)/15, or 2/3 of a mile from the house.

[RIPP_n_WIPE]

Wow thanks.

[Surlethe]

B = 5t
A = 2(t + 0.2)

Time of intersection: A = B so 5t = 2(t + 0.2) implies 3t = 0.4, so t = 2/15 hr = 8 min. Distance of intersection: 5*2/15 mi = 10/15 mi = 2/3 mi.

The conceptual part is probably the most difficult: set your origin when \textit{Bob} leaves the house. Then Alice's equation of motion is A = 2(t+0.2): since she's already traveled for 12 minutes = 0.2 hr, she's gone 2*0.2 miles. You can set the origin when Alice leaves the house, but then you have to deal with a bent function when Bob starts to jog.

[Singular Intellect]

Was it silly for me to immediately be suspicious of the question, since there was no stated distance between the houses in question, thus Alice could've arrived at it well before Bob left and any interception point was based purely on a unsubstantiated assumption?

[CaptainChewbacca]

Was it silly for me to immediately be suspicious of the question, since there was no stated distance between the houses in question, thus Alice could've arrived at it well before Bob left and any interception point was based purely on a unsubstantiated assumption?

For the question to be answerable, you have to assume they will meet before they arrive at the friend's house. I'm sure the friend could be next door, but there's no way to do that.