Bill travels first 40% of the distance to his destination at 80 mph and covered the balance distance at 40 mph. What is the average speed of his travel?When we have these Average Rate for the whole trip problems, the key is to understand that:

- We only need the Rates of both part of the trips.

- We can plug in for Distance and infer for Time

- Then, you just have to solve the simple formula (Distance 1 + Distance 2) / (Time 1 + Time 2)

I´ll tell you how I did this in around 75 seconds with the RTD chart

Question Stem

R * T = D1st Part: 80 * ? =(0.4) d

2nd Part: 40 * ? =(0.6) d

Note that Rates, Times, and Distances ARE ALL DIFFERENT in each part of the trip.

Next, come up with some Distances to plug in (400 and 600 are a safe bet here)

R * T = D1st Part: 80 * ? = 400

2nd Part: 40 * ? =600

Now, deduce the Times for each part of the trip

R * T = D1st Part: 80 * 5 = 400

2nd Part: 40 * 15 =600

Now, solve the Average Rate Formula

(400 + 600) / (5 + 15) = 1,000/20 = 50

I know it looks time consuming but this is just because I broke every step down. You obviously don´t need to do 3 charts: it is just the same chart in each step of the resolution.

Hope it helps!

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