AboutAbe Mantell Expertise Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!
Experience Over 15 years teaching at the college level.
Organizations belong to NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.
Education/Credentials B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook
I have the following problem:
Two people A & B start walking towards each other by road connecting city1 and city2.
A starts exactly at noon from city1 to city2. B starts exactly at 2 p.m. from city2 towards
city1.
Both meet at a place at five past four and continues their journey. If after meeting with
each other, they take exactly same time to reach their destinations, at what time they will
reach to their destinations?
What I worked:
A walks for nearly 4hrs B walked for 2hrs. Speed of B is twice that of A. After meeting, A
will take 4 more hrs because B took 2 hrs to complete that distance. So,they should reach by
8p.m.
but answer is 7 p.m.
So,can you please guide me?
Answer Hello Adi,
Let a=the rate at which person A travels (units/minute)
and b=the rate at which person b travels.
Also, let's call the distance from City I to City II 1 unit.
By the time they meet, person A traveled for 245 minutes, and person B
for 125 minutes. Person A traveled a distance of 245a and person B
traveled 125b, the sum of those distances must equal 1 unit (the distance
between the two cities). Thus, one equation is:
1. 245a + 125b = 1
Then it takes them the same amount of time to travel the remaining distance.
So, person A travels the distance 125b in 125b/a units of time, and
person B travels the distance 245a in 245a/b units of time, which must
be equal. Thus, a second equation is
2. 245a/b = 125b/a ==> 245a^2 - 125b^2 = 0, dividing by 5 gives
. 49a^2 - 25b^2 = 0, which factors to (7a-5b)(7a+5b)=0
. Thus, either 7a-5b=0 or 7a+5b=0. Only 7a-5b=0 yields positive
. values for both a and b. Therefore, b/a=7/5. Substituting that
. into the expression 125b/a being the time in minutes they both need
. to finish the trip ==> 125(7/5)=175 minutes=2 hrs 55 min.
So, 2 hrs 55 min after 4:05 Pm, they will both reach their destinations,
which is 7 PM.
