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Jaquan passed a checkpoint jogging at a constant speed of 9(km)/(h). Then, 2 minutes later, Odalis passed the same checkpoint.
If Odalis runs at a constant speed of 12(km)/(h), then how far past the checkpoint will Odalis be when they catch up to Jaquan?

◻km

Jaquan passed a checkpoint jogging at a constant speed of 99kmh\frac{\text{km}}{\text{h}}. Then, 22 minutes later, Odalis passed the same checkpoint.\newline If Odalis runs at a constant speed of 1212kmh\frac{\text{km}}{\text{h}} then how far past the checkpoint will Odalis be when they catch up to Jaquan?\newlinekm\square \,\text{km}

Full solution

Q. Jaquan passed a checkpoint jogging at a constant speed of 99kmh\frac{\text{km}}{\text{h}}. Then, 22 minutes later, Odalis passed the same checkpoint.\newline If Odalis runs at a constant speed of 1212kmh\frac{\text{km}}{\text{h}} then how far past the checkpoint will Odalis be when they catch up to Jaquan?\newlinekm\square \,\text{km}
  1. Calculate Speed Difference: Jaquan's speed is 9km/h9\,\text{km/h} and Odalis's speed is 12km/h12\,\text{km/h}. The difference in their speeds is 12km/h9km/h=3km/h12\,\text{km/h} - 9\,\text{km/h} = 3\,\text{km/h}.
  2. Convert Time to Hours: Odalis starts 22 minutes after Jaquan. Convert 22 minutes to hours to match the speed units. 22 minutes = 260\frac{2}{60} hours = 130\frac{1}{30} hours.
  3. Calculate Jaquan's Distance: In 130\frac{1}{30} hours, Jaquan will have covered a distance of 9km/h×130hours=930km=0.3km.9 \, \text{km/h} \times \frac{1}{30} \, \text{hours} = \frac{9}{30} \, \text{km} = 0.3 \, \text{km}.
  4. Calculate Time to Catch Up: Now, calculate the time it takes for Odalis to catch up to Jaquan. Since Odalis is running 3km/h3 \, \text{km/h} faster, the time to catch up is the distance Jaquan covered divided by the speed difference. Time = 0.3km3km/h=0.1hours\frac{0.3 \, \text{km}}{3 \, \text{km/h}} = 0.1 \, \text{hours}.
  5. Calculate Odalis's Distance: Calculate the distance Odalis covers in 0.10.1 hours at a speed of 1212 km/h. Distance = Speed ×\times Time = 1212 km/h ×\times 0.10.1 hours = 1.21.2 km.

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