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Skill BuildeWatch the video and then solve the problem given below.Click here to watch the videoMargaret drove to a business appointment at 40 mph. Her average speed on the return trip was 30 mph. The return trip took 1/3 hour longer because of heavy traffic. How far did she travel to theappointment?She traveled milesEnter your answer in the answer box and then click Check Answer.All parts showing

Respuesta :

Let's call the distance to the appointment 'd', and the time of the first travel (going to the appointment) 't'.

Now, we need to use the formula for the distance:

[tex]\text{distance}=\text{average speed }\cdot\text{ time}[/tex]

For the first part of the trip, we have the distance 'd', the average speed is 40 mph and the time is 't':

[tex]d=40\cdot t[/tex]

Then, for the second part of the trip (return trip), the distance is also 'd', the average speed is 30 mph, and the time is 't + 1/3', because she took 1/3 hour longer than the first trip.

So we have that:

[tex]d=30\cdot(t+\frac{1}{3})=30t+10[/tex]

Now, we just need to equate both 'd':

[tex]\begin{gathered} 40t=30t+10 \\ 10t=10 \\ t=1 \end{gathered}[/tex]

So the time 't' is 1 hour. Now we can use that to find the distance 'd':

[tex]d=40t=40\cdot1=40[/tex]

So the distance to the appointment is 40 miles.

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