Two friends A and B leave point A and point B simultaneously and travel towards Point B and Point A on the same route at their respective constant speeds. They meet along the route and immediately proceed to their respective destinations in 32 minutes and 50 minutes respectively. How long will B take to travel the entire journey between Point B and point A?
Choose the correct choice from the following.
A) 65 B) 70 C) 90 D) 75 E) 80
Let x per minute be the speed of A and y per minute be the speed of B.   After meeting at a point, A travels for 32 mins and B travels for 50 mins. So distance covered by each of them post point of crossing   A= 32x and B=50y   The distance covered by A and B before they cross each would be distance covered by B and A post crossing respectively.   Therefore distance covered by B before he meets A= 32x   Time taken by B cover 32x distance= 32x/y mins   Therefore total time taken by B= 32x/y + 50 mins ................. I   We need to find value of x in terms of y to arrive at final answer.   Total distance= 32x+50y   Combined speed of A and B= x+y   Therefore time taken before A and B meet en-route= (32x+50y)/(x+y)   Time taken by B reach destination after meeting A= 50 mins   Total travel time for B= [(32x+50y)/(x+y)]+50 mins ...................II   Equate I and II   32x/y+50= [(32x+50y)/(x+y)]+50   (32x+50y)/y=(82x+100y)/(x+y)   32x^2+50xy+32xy+50y^2=82xy+100y^2   32x^2+82xy-82xy+50y^2-100y^2=0   32x^2-50y^2=0   32x^2=50y^2   16x^2=25y^2   Taking square root.. (since x and y denote speed, square root can't be negative)   4x=5y   y=4x/5 ............ III   substitute in I   =32x/(4x/5) + 50   =32x*5/4x + 50   =40+50= 
<gadget id="calculator">40+50</gadget>
<output>90</output>
90 mins   90
<result>C</result>
Two friends A and B leave point A and point B simultaneously and travel towards Point B and Point A on the same route at their respective constant speeds. They meet along the route and immediately proceed to their respective destinations in 32 minutes and 50 minutes respectively. How long will B take to travel the entire journey between Point B and point A?