Did You Find Out? Get the Answer to the Riddle of E-News Issue No. 2, March 2023

In 10 minutes (= 600 seconds), Tom runs 600/x laps and needs t seconds to complete 1 lap. If, for example, he needed exactly 50 seconds for 1 lap, he would do 12 laps within 10 minutes (600/50 = 12). Mike is faster and needs 8 seconds less for 1 lap, meaning (t – 8) seconds. By the time he outruns Tom, Mike is 30 seconds ahead (570 seconds), and runs one more lap than the slower Tom.

x = Number of laps
t = Time for one of Tom's lap

Step 1: Equation for Tom

x * t = 10 minutes (600 seconds)
x = 600 seconds/ t

Step 2: Equation for Mike

(x + 1) * (t – 8 seconds) = 10 minutes – 30 seconds = 570 seconds

Step 3: Insert equation 1 into equation 2

(600 /t +1) * (t – 8) = 570
(600 * t – 4800)/ t + t – 8 = 570
600 – 4800/ t +t = 578
22t – 4800 + t2 = 0
t2 + 22t – 4800 = 0

Step 4: Find the solution with the help of the quadratic formula

x₁ = - 22/2 +  √(484/4 + 4800) = 59.15
x₂ = - 22/2 - √(484/4 + 4800) = - 81.15

X₂ is useless, because seconds can only be positive. Tom needed 59.15 seconds per lap, while Mike needed 8 seconds less, or 51.15 seconds. By the time he outruns Tom, Mike has run (570/51,15) 11.1 laps and Tom has run (600/59,15) 10.1 laps.