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
A) 90  B) 80  C) 75  D) 60  E) 65
<gadget id="calculator">50 * 32</gadget>
<output>1_600</output>

<gadget id="calculator">1_600 ** (1/2)</gadget>
<output>40</output>

<gadget id="calculator">40 + 50</gadget>
<output>90</output>

<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?
add(sqrt(multiply(50, 32)), 50)
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 = 32 x and d = 50 y 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 = 32 x time taken by d cover 32 x distance = 32 x / y mins therefore total time taken by d = 32 x / y + 50 mins . . . . . . . . . . . . . . . . . i we need to find value of x in terms of y to arrive at final answer . total distance = 32 x + 50 y combined speed of c and d = x + y therefore time taken before c and d meet en - route = ( 32 x + 50 y ) / ( x + y ) time taken by d reach destination after meeting c = 50 mins total travel time for d = [ ( 32 x + 50 y ) / ( x + y ) ] + 50 mins . . . . . . . . . . . . . . . . . . . ii equate i and ii 32 x / y + 50 = [ ( 32 x + 50 y ) / ( x + y ) ] + 50 ( 32 x + 50 y ) / y = ( 82 x + 100 y ) / ( x + y ) 32 x ^ 2 + 50 xy + 32 xy + 50 y ^ 2 = 82 xy + 100 y ^ 2 32 x ^ 2 + 82 xy - 82 xy + 50 y ^ 2 - 100 y ^ 2 = 0 32 x ^ 2 - 50 y ^ 2 = 0 32 x ^ 2 = 50 y ^ 2 16 x ^ 2 = 25 y ^ 2 taking square root . . ( since x and y denote speed , square root ca n ' t be negative ) 4 x = 5 y y = 4 x / 5 . . . . . . . . . . . . iii substitute in i = 32 x / ( 4 x / 5 ) + 50 = 32 x * 5 / 4 x + 50 = 40 + 50 = 90 mins a