If in a race over a distance of $d$ meters at uniform speed, A can beat B by 20 meters, B can beat C by 10 meters and A can beat C by 28 meters, then $d$, in meters, is equal to

When A runs d meters, B runs d minus 20 meters, so the ratio of their speeds is d over (d minus 20). Similarly, when B runs d meters, C runs d minus 10 meters, giving the ratio of their speeds as d over (d minus 10). When A runs d meters, C runs d minus 28 meters, so d divided by (d minus 28) equals the product of the two ratios, which is d squared divided by the product of (d minus 20) and (d minus 10). Simplifying this gives d minus 28 equals d minus 20 times d minus 10 all divided by d, which leads to 2d equals 200. Therefore, d is equal to 100.

• Thanks
• Wrong explanation