A car runs 56m/h for uphill, 78m/h for straight surface, 87m/h for downhill. It takes 4 hours for the car to travel from A to B and 4 hours 40 minutes from B to A. Now, what's the distance from A to B? didn't find this teaser on the board, have fun guys.

322.839 miles

Between 295.273 & 322.839 depending on the length of the flat portion.If s = length of flat portion then it is d(A,B) = 295.273 + 0.126412 s

Can someone explain the solution with equations?Thanks.Mike

Here is how I came to it: let u, s & d be the total length of the uphill, straight & downhill porions as we travel from A to B.And let Vu, Vs & Vd be 56, 78 & 87 respectively for the speeds in those situations.Then from A to B and B to A the times are (noting that uphill becomes downhill & vice versa on the way back):u/Vu + s/Vs + d/Vd = time(A,B) = 4u/Vd + s/Vs + d/Vu = time(B,A) = 4+2/3Solving the system of u & d on the left we get solutions in terms of s:u = 812/57629( 6760 - 31s ) = 95.2493 - 0.436794 sd = 812/57629( 14196 - 31s ) = 200.023 - 0.436794 sAnd u + d + s = 295.273 + 0.126412 s with the fact thats is limited by s <= Min( 95.2493/0.436794, 200.023/0.436794 ) = 218.065 as u, d >= 0.

Thanks aym! I found a neat solution by making d = u^2 from A to B. Solution is u = 10.748 miles, s = 193.458, and d = 115.5223 for a total distance of 319.728 miles. A to B is exactly 4 hours, and B to A is exactly 4.66666 hours.Nice problem!Mike

Hello Mensa,While your solution meets the constraints as per Aym' ssolution, I was wonder what prompted you to think to set d = u^2. Thanks for any clarification,Vivek

Hello vsatsang - I chose d=u^2 'cause I'm lazy I guess. As long as I have d as a function of u, I have two equations and two unknowns. The squaring gives me a quadratic (easily solved!!).There are a whole lot of other interesting solutions to this, (e.g. d=u^3). Neat problem!Mike

Hi aym,can you explain this?"with the fact thats is limited by s <= Min( 95.2493/0.436794, 200.023/0.436794 )"Thx

QuoteOriginally posted by: ZecitimanHi aym,can you explain this?"with the fact thats is limited by s <= Min( 95.2493/0.436794, 200.023/0.436794 )"ThxHi Zecitiman, that is because u,d,s are all non-negative quantities being distances.From the two equations you get two overlapping constraints on s, the stricter of which prevails.