Deniel's average speed for the total
distance is 3.6 mph
Average speed is difined as the total distance travelled divided by the total time required to cover the distance. Mathematically, it is expressed as:
[tex]Ave. Speed = \frac{Total distance }{Total time}[/tex]
To obtain the average speed of Daniel, we shall determine the distance travelled in each case. This is illustrated below:
Case 1:
Speed 1 (S₁) = 6 mph
Time 1 (t₁) = 0.8 h.
Distance 1 (D₁) =?
[tex]Speed = \frac{Distance}{Time} \\\\S_{1} = \frac{D_{1}}{t_{1}} \\\\6 = \frac{D_{1}}{0.8}[/tex]
Cross multiply
D₁ = 6 × 0.8
D₁ = 4.8 mile
Case 2:
Speed 2 (S₂) = 2 mph
Time 2 (t₂) = 1.2 h.
Distance 2 (D₂) =?
[tex]S_{2} = \frac{D_{2}}{t_{2}}\\\\2 = \frac{D_{2}}{1.2}[/tex]
Cross multiply
D₂ = 2 × 1.2
D₂ = 2.4 mile
Next, we shall determine the total time. This can be obtained as follow:
Time 1 (t₁) = 0.8 h.
Time 2 (t₂) = 1.2 h.
Total time (T) =?
T = t₁ + t₂
T = 0.8 + 1.2
T = 2 h
Next, we shall determine the total distance. This can be obtained as follow:
Distance 1 (D₁) = 4.8 mile
Distance 2 (D₂) = 2.4 mile
Total distance (D) =?
D = D₁ + D₂
D = 4.8 + 2.4
D = 7.2 mile
Finally, we shall determine the average speed of Daniel. This can be obtained as follow:
Total time = 2 h
Total distance = 7.2 mile
Average speed =?
[tex]Ave. speed = \frac{Total distance }{Total time} \\\\Ave. speed = \frac{7.2 }{2}[/tex]
Average speed = 3.6 mph
Therefore, the average speed of Daniel is 3.6 mph
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