Question

On the first part of a 218 mile trip, a salesperson travels 2 hours and 15 minutes at an average speed of 64 mph. The salesperson needs to arrive at the destination in another hour and 20 minutes. Find the average speed required for the remainder of the trip. Round your answer to one decimal place. No units should be added to your answer.

Answer 1

The speed of an object is its distance traveled per unit time

The average speed required for the remainder of the trip 55.5

The reason the average speed value is correct is given as follows:

The known parameters;

The length of the first part of the trip, L = 218 mile

Duration of the time the sales person travels, t₁ = 2 hours and 15 minute

Average speed of travel, v₁ = 64 mph

The time at which the salesperson arrive at the destination, t₂ = 1 hour and 20 minutes

Required:

To find the average speed required for the remainder of the trip

Solution:

Distance traveled = Speed × Time

The distance traveled on the first part of the trip, d₁ = v₁ × t₁

(t₁ = 2 hours and 15 minute = 2.25 hours)

∴ d = 64 mph × 2.25 hours = 144 miles

The distance of the remainder part of the trip, d₂ = L - d₁

d₂ = 218 mile - 144 mile = 74 mile

The average speed required for the remainder of the trip, v₂, is given as follows;

$v_2 = \dfrac{d_2}{t_2}$

t₂ = 1 hour and 20 minutes = $1\frac{1}{3} \ hour = \frac{4}{3} \, hour$

Therefore;

$v_2 = \dfrac{74 \ mile}{1\frac{1}{3} \ hour} = 55.5 \ mph$

With the units left out, we have;

The average speed required for the remainder of the trip, v₂ = 55.5

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