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

Question

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

Bytelearn · Accepted Answer

Calculate Jaquan's Distance: First, we need to determine how far Jaquan has traveled by the time Odalis starts. Since Jaquan is traveling at 9 km/h, we need to convert the 2 minutes into hours to calculate the distance.Convert Time to Hours: To convert 2 minutes into hours, we divide by 60 (since there are 60 minutes in an hour). 2 minutes ÷ 60 minutes/hour = 1/30 hourCalculate Jaquan's Distance: Now we calculate the distance Jaquan has traveled in 1/30 hour at a speed of 9 km/h. Distance = Speed × Time Distance = 9 km/h × 1/30 hourFind Time for Odalis to Catch Up: Perform the multiplication to find the distance. Distance = 9 km/h × 1/30 hour = 9/30 km = 0.3 km Jaquan has traveled 0.3 km in the 2 minutes before Odalis starts.Solve for Time: Next, we need to find out how long it will take for Odalis to catch up to Jaquan. Since they are both moving at a constant speed, we can set up an equation where the distance Odalis travels is equal to the distance Jaquan travels plus the 0.3 km head start. Let t be the time in hours it takes for Odalis to catch up to Jaquan after Odalis starts. Distance Odalis travels = Distance Jaquan travels + 0.3 km 12 km/h × t = 9 km/h × t + 0.3 kmCalculate Odalis's Distance: Now we solve for t. 12t = 9t + 0.3 12t - 9t = 0.3 3t = 0.3 t = 0.3 / 3Calculate Odalis's Distance: Perform the division to find the time t. t = 0.3 / 3 = 0.1 hours It will take Odalis 0.1 hours to catch up to Jaquan.Finally, we calculate the distance Odalis will have traveled in 0.1 hours at a speed of 12 km/h. Distance = Speed × Time Distance = 12 km/h × 0.1 hourPerform the multiplication to find the distance. Distance = 12 km/h × 0.1 hour = 1.2 km Odalis will be 1.2 km past the checkpoint when they catch up to Jaquan.

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