SOLUTION: A leaves Mumbai at 6am and reaches Bangalore at 10am. B leaves Bangalore at 8am and reaches Mumbai at 11:30am. At what time do they cross each other ?

Algebra ->  Exponents -> SOLUTION: A leaves Mumbai at 6am and reaches Bangalore at 10am. B leaves Bangalore at 8am and reaches Mumbai at 11:30am. At what time do they cross each other ?      Log On


   

Question 887065: A leaves Mumbai at 6am and reaches Bangalore at 10am. B leaves Bangalore at 8am and reaches Mumbai at 11:30am. At what time do they cross each other ?
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
The distance between Mumbai and Bangalore is 987 Km
We use rate times time = distance
let Ra be the rate of A
let Rb be the rate of B
Time for A to cover the 987 Km is 4 hours
Time for B to cover he 987 Km is 3.5 hours
therefore we have two equations
Ra * 4 = 987
Ra = 987 / 4 = 246.75 Km per hour
Rb * 3.5 = 987
Rb = 987 / 3.5 = 282 Km per hour
note that A has been travelling for two hours before B gets started, therefore we must subtract 2*246.75 from 987
987 - 2*246.75 = 493.5
now A and B cross when together they have covered 493.3 Km, therefore we have
note that t = time we are interested in
246.75t + 282t = 493.5
528.75t = 493.5
t = 493.5 / 528.75
t = 0.933333333 hour
convert t to minutes
t = 0.933333333 * 60 = 56 minutes
we will now add 56 minutes to B's start time of 8am
therefore the time A and B cross is 8:56 am