Question

Jody enters a 12 km race. She wants to finish the race in one hour and twenty minutes. She starts off jogging at a speed of 7 km/h. After 30 minutes, she realizes that she needs to increase her speed to finish the race in her desired time. For the remaining time, what speed she must run at to finish the race in the exactly one hour and twenty minutes

Answer 1

$Total \: distance \:of \:the \:race (d) = 12 \:km$

$Time \:to \: finish \: the \: race(T)\\ = 1 \:hour \: 20 \: minutes$

Case 1:

$Speed \: of \: Jody = 7 \: kmph$

$Time(t_{1}) = 30 \: minutes = \frac{1}{2} \: hour$

$Distance \: travelled (d_{1}) = speed \times time \\= 7 \times \frac{1}{2} \\= 3.5 \: km$

Case 2:

$Remaining \:distance = d - d_{1} \\= 12 \:km - 3.5 \:km \\= 8.5 \:km$

$Time = T - t_{1}\\ = 1\:hour \: 20 \: minutes - 30 \: minutes\\= 50 \: minutes \\= \frac{50}{60} \: hours \\= \frac{5}{6} \:hours$

$Speed \:to \:finish \:the \:race = \frac{distance}{time } \\= \frac{8.5}{\frac{5}{6}}\\= 8.5 \times \frac{6}{5} \\= 10.2 \: kmph$

Therefore.,

$\red {Speed \:to \:finish \:the \:race} \green { = 10.2 \: kmph }$

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