Question

1. jamie and michael were debating who could walk the fastest. they compared their speeds over a camping trip:

jamie hiked 31 km in 6.0h, while michael hiked 42 km in 7.5h.
a. what were their speeds (in km/h)? who was the fastest? (5 marks)
b. if both continued with their original speeds, how far could each of them get if they travelled 3.0 hours? (4 marks)
c. if both continued with their original speeds, how long would it take each of them to travel 50km? (4 marks)

Explanation:

Part a

Step1: Calculate Jamie's speed

Speed formula: \( v = \frac{d}{t} \), where \( d \) is distance, \( t \) is time. For Jamie, \( d = 31 \, \text{km} \), \( t = 6.0 \, \text{h} \).
\( v_{\text{Jamie}} = \frac{31}{6.0} \approx 5.17 \, \text{km/h} \)

Step2: Calculate Michael's speed

For Michael, \( d = 42 \, \text{km} \), \( t = 7.5 \, \text{h} \).
\( v_{\text{Michael}} = \frac{42}{7.5} = 5.6 \, \text{km/h} \)

Step3: Compare speeds

\( 5.6 > 5.17 \), so Michael is faster.

Step1: Distance for Jamie

Use \( d = v \times t \). \( v_{\text{Jamie}} \approx 5.17 \, \text{km/h} \), \( t = 3.0 \, \text{h} \).
\( d_{\text{Jamie}} = 5.17 \times 3.0 \approx 15.51 \, \text{km} \)

Step2: Distance for Michael

\( v_{\text{Michael}} = 5.6 \, \text{km/h} \), \( t = 3.0 \, \text{h} \).
\( d_{\text{Michael}} = 5.6 \times 3.0 = 16.8 \, \text{km} \)

Step1: Time for Jamie

Use \( t = \frac{d}{v} \). \( d = 50 \, \text{km} \), \( v_{\text{Jamie}} \approx 5.17 \, \text{km/h} \).
\( t_{\text{Jamie}} = \frac{50}{5.17} \approx 9.67 \, \text{h} \)

Step2: Time for Michael

\( v_{\text{Michael}} = 5.6 \, \text{km/h} \).
\( t_{\text{Michael}} = \frac{50}{5.6} \approx 8.93 \, \text{h} \)

Answer:

Jamie's speed: \( \approx 5.17 \, \text{km/h} \), Michael's speed: \( 5.6 \, \text{km/h} \). Michael was the fastest.

Part b