how do u do this?!?

Question

can anyone explain how to do this question?



Mary cycled off in another direction on Saturday morning. She left her home at 9 am and cycled 60 miles at a constant speed of 7 miles per hour until she reached a guesthouse. She spent Saturday night in the guesthouse and cycled back home on Sunday morning, starting from the guesthouse at 9 am and cycling back home along the same route as the day before at a constant speed of 13 miles per hour.

The solution of a well-known puzzle says that Mary will pass some point along the route at exactly the same time on both Saturday and Sunday. How many hours after 9 am will this happen?

TIP: When you've figured out the time, remember to check that Mary will be the same distance from home at that time on both days.

morningfoxnorth,wat do u mean by
7H miles or 13H miles in

"Then Mary#1 will be 7H miles from home, and
Mary#2 will be 60 - 13H miles from home."

is dat suposd to b 7 (and de that hours passed?) miles?
wat do u do with the H after de 7 ?

^^^^^^^^oh i get it!lol

Answer 1

The part about Saturday and Sunday is just to confuse you.

Think of it like this: Mary#1 has a twin, Mary#2.
Mary#1 leaves home at 9:00. Mary#2 leaves the guesthouse at 9:00, on the same day. Soon or later, they will meet.

Lets say they meet after 'H' hours.
Then Mary#1 will be 7H miles from home, and
Mary#2 will be 60 - 13H miles from home.

.... 7H means 7 multiplied by the number H
.... 13H means 13 multiplied by the number H

So solve 7H = 60 - 13H.

Answer 2

Well, this is a nice little question...

Mary will reach the same point on the route both days exactlly at noon. Here is why:

As he starts from home, her distance from home, let's designate it S1, rises according the law V1 * T1, where V1, 7 miles per hour, is her velocity, and T1, in hours, time she spent on travel.

Returning from guesthouse, her distance from guesthouse, S2, will be, similarly, V2 * T2, where V2 is new speed, 13 mph.

Apparently, S1 + S2 = 60 miles, so S1 = 60 - S2, so we have:

S1 = V1 * T1
S2 = 60 - S1 = V2 * T2

Since we want to find time when she was in the same point, we can write T1 = T2 = T; therefore:

V1 * T = 60 - V2 * T

T = 60 / (V1 + V2) = 60 / (7 + 13) = 3.

Since she started from home and guesthouse at 9 a.m. both days, this result means that she reached the same place on the route at (9+3) = 12 hours, i.e., at noon.

Update:

Oh, yes, and you can check it:

First day, she travels 7 miles per hour, so untill noon (for 3 hours), she will be at point 7 * 3 = 21 miles far from home; in Sunday, she travels 13 miles per hour, so untill noon (again 3 hours), she passes 3 * 13 = 39 miles; she is 39 miles far from guesthouse, and it is 60 - 39 = 21 miles from home, so she is in the same point, isn't she!

Answer 3

Let d be the distance she is from home.

Let t be the time -- actually, it's easier to let t be the number of hours passed since 9 am.

On each of Saturday and Sunday, you can find an equation for d as a function of t. So solve those two equations for t and d.

They will involve fractions, but don't let that scare you.