Others Maths Puzzle

A hill of 440 yards is there. Two competitors JACK and JILL go up the hill, first JACK reaches the topmost and immediatly starts back and meet JILL 20 yards from the topmost point. Finally JACK reaches the starting point 0.5 minutes earler than JILL. Speed while coming down is 1.5 times the speed of going up. Find the time taken by JACK for whole journey (880 yards)?

Read Solution (Total 2)

Jack took 6.3 minutes.
12 years agoHelpfull: Yes(1) No(3)

6.3 minutes
Let jack moves with velocity v1, time t11 upward t12 downward
Jill moves with velocity v2, time t21 upward and t22 downward
Jack and Jill mee at a time say t, so at that time 440/v1+20/v1*1.5 = 420/v2*1.5.
from the above equation v1/v2=68/63 = t21/t11 = t22/t12
t21=68/63*t11 and t22 = 68/63*t21
give t21+t22 = t11+t12+0.5 => 68/63*t11+68/63*t12=t11+t12+0.5
68(t11+t12)=63(t11+t12)+0.5*63
=>5(t11+t12)=0.5*63 => t11+t12 = 63*0.5/5 => t11+t12 = 6.3
total time taken by JACK is t11(up)+t12(down) = 6.3
10 years agoHelpfull: Yes(1) No(1)

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