Two friends C and D leave point C and point D simultaneously and travel towards Point D and Point C 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 D take to cover the entire journey between Point D and point C?
Choose the correct choice from the following answers:	A) 90	B) 80	C) 75	D) 60	E) 65
Let x per minute be the speed of C and y per minute be the speed of D.   After meeting at a point, C travels for 32 mins and D travels for 50 mins. So distance covered by each of them post point of crossing   C= 32x and D=50y   The distance covered by C and D before they cross each would be distance covered by D and C post crossing respectively.   Therefore distance covered by D before he meets C= 32x   Time taken by D cover 32x distance= 32x/y mins   Therefore total time taken by D= 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 C and D= x+y   Therefore time taken before C and D meet en-route= (32x+50y)/(x+y)   Time taken by D reach destination after meeting C= 50 mins   Total travel time for D= [(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>A</result>
Two friends C and D leave point C and point D simultaneously and travel towards Point D and Point C 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 D take to cover the entire journey between Point D and point C?