Answer:
51 mph
Step-by-step explanation:
→ The first thing we need is a formula which links speed, distance and time so,
Speed = Distance ÷ Time
Speed = mph
Distance = metres/miles
Time = hours
→ Since we want to work out the average speed of the entire journey we need to first work out the total distance and total time. Using the first sentence of the paragraph, it says that <em>the car travels at an average speed of 45 mph for 40 minutes, </em>we can rearrange the formula to work out the distance so,
Speed = Distance ÷ Time
→ Rearrange to get distance as subject
Distance = Speed × Time
→ Substitute in the values
Distance = 45 × 40
→ Remember that the time is hours but we substituted in minutes so we divide the time value by 60
40 ÷ 60 = 0.666666667
→ Substitute in the time value multiplied by the speed
Distance = 45 × 0.666666667 = 30
⇒ 30 metres/miles is overall distance for the first part of the journey
→ Now we have to work out the distance for the second part of the journey. State the distance formula.
Distance = Speed × Time
→ Substitute in the values into the distance formula
Distance = 60 × 25
→ Remember that the time is hours but we substituted in minutes so we divide the time value by 60
25 ÷ 60 = 0.416666667
→ Substitute in the time value multiplied by the speed
Distance = 60 × 0.416666667 = 25
⇒ 25 metres/miles is overall distance for the second part of the journey
→ Now we have to add the distance of both the journeys together
25 + 30 = 55
→ Then we add the times of the journey together
40 minutes + 25 minutes = 65 minutes
→ Convert 65 minutes into hours
65 ÷ 60 = 1.08333 hours
→ Substitute both values into the speed = distance ÷ time formula
Speed = 55 ÷ 1.08333 = 50.76923077
→ The question says to round it to the nearest whole number so,
50.76923077 = 51 mph
,
denotes the nth partial sum
is the first term (in our case it is 0)
is the common difference (difference in term and the previous term) (in our case it is 0.5)