P cycles at a speed of 4 m/s for the first 8 seconds, 5 m/s for the next 8 seconds, 6 m/s for the next 8 and so on. Q cycles at a constant speed of 6.5 m/s throughout. If P and Q had to cycle for a 400 m race, how much lead in terms of distance, can P give Q and still finish at the same time as Q? Choose one.
A) 43.4 m
B) 56.6 m
C) 32.1 m
D) P cannot give a lead as Q is always ahead of P
E) None of these
DETAILED SOLUTION   Distance covered by P in 8 sec = 4 * 8= 
<gadget id="calculator">4 * 8</gadget>
<output>32</output>
32 m   Distance covered by P in 16 sec= 32 + 5 *8= 
<gadget id="calculator">32 + 5 *8</gadget>
<output>72</output>
72 m   Distance covered by P in 24 sec= 72 + 6 * 8= 
<gadget id="calculator">72 + 6 * 8</gadget>
<output>120</output>
120 m   Distance covered by P in 32 sec= 120 + 7 * 8= 
<gadget id="calculator">120 + 7 * 8</gadget>
<output>176</output>
176 m   Distance covered by P in 40 sec= 176 + 8 * 8= 
<gadget id="calculator">176 + 8 * 8</gadget>
<output>240</output>
240 m   Distance covered by P in 48 sec= 240 + 9 * 8= 
<gadget id="calculator">240 + 9 * 8</gadget>
<output>312</output>
312 m   Total distance in 48 sec= 312m   To cover balance 86 m with speed = 10 m/sec, time taken = 86/10= 
<gadget id="calculator">86/10</gadget>
<output>43/5 = around 8.6</output>
8.6 sec   So P would finish 400 m in 48 + 8.6= 
<gadget id="calculator">48 + 8.6</gadget>
<output>56.6</output>
56.6 seconds.   In 56.6 seconds, Q cycles  56.6 * 6.5= 
<gadget id="calculator"> 56.6 * 6.5</gadget>
<output>367.9</output>
367.9 m or B should have a 32.1 m lead to result in a dead heat.   32.1 mORRE32.1 mT ANSWER 32.1 m
<result>C</result>
P cycles at a speed of 4 m/s for the first 8 seconds, 5 m/s for the next 8 seconds, 6 m/s for the next 8 and so on. Q cycles at a constant speed of 6.5 m/s throughout. If P and Q had to cycle for a 400 m race, how much lead in terms of distance, can P give Q and still finish at the same time as Q?