Question

Julia and Kajal make deliveries on their bicycles. For each delivery, they need some time to get ready, and then they each ride at a constant speed.

Julia takes 40 minutes to make a delivery 5 kilometers away. She uses 10 minutes of the delivery time to get ready

The time it takes Kajal to make a delivery (in minutes) as a function of the distance of the delivery (in kilometers) is given by the following function:

T(d)=15+6d

Who takes more time to get ready?

Who rides faster?

Answer 1

Kajal takes longer to get ready than Julia, as Kajal's preparation time is 15 minutes compared to Julia's 10 minutes. Both Julia and Kajal ride at the same speed of 10 km/h, as they both take 30 minutes to complete a delivery over a distance of 5 kilometers, excluding preparation time.

Step-by-step explanation:

To determine who takes more time to get ready for the deliveries, we compare the preparation time of Julia and Kajal. From the information provided, Julia takes 10 minutes to get ready. Kajal's preparation time can be found from her delivery time function T(d) = 15 + 6d, where 15 represents the fixed time she takes to get ready, regardless of the delivery distance. Therefore, Kajal takes longer to get ready compared to Julia.

To find who rides faster, we need to calculate the riding speeds of both Julia and Kajal. Julia's riding time is 30 minutes (40 minutes total delivery time minus 10 minutes preparation time) for a distance of 5 kilometers. Julia's speed is then 5 km divided by 0.5 hours (30 minutes), which is 10 km/h. For Kajal, we must compare her speed for any given distance, d, by subtracting her preparation time from the total time. For a 5 km delivery, Kajal's time would be T(5) = 15 + 6(5) = 45 minutes, but the actual riding time is 45 - 15 = 30 minutes. Hence, for 5 kilometres, Kajal also rides at a speed of 5 km divided by 0.5 hours, resulting in 10 km/h as well. Therefore, both Julia and Kajal ride at the same speed.

Answer 2

For Julia’s case, we determine first he time it takes her to ride or cover every kilometre knowing that 10 minutes of the given 40 minutes is used for the preparation.

r (Julia) = (40 – 10 min) / 5 km = 6 minutes per kilometre

A. The time it takes Julia to get ready is only 10 minutes while from the given equation, the time it takes Kajal to get ready is 15 minutes. Hence, the answer is Kajal.

B. From the calculation above, it takes Julia 6 minutes to cover a kilometre. From the equation, it is also given that Kajal takes 6 minutes to cover every kilometre. Hence, the answer is Neither as they travel at the same rate.