Question

37. Construct Arguments Luis and Raul are

Answer 1

Using the slope - intercept relation, the required equation which models the scenario and Raul's speed are ;

• y = - 7.5x + 15
• 4 miles per hour

Time difference, Δt = 1.2 hours - 0.5 hours = 0.7 hours

Change in distance, Δd = 11.25 - 6 = 5.25 miles

Assuming a constant speed :

• Speed = (Δd ÷ Δt) = (5.25 ÷ 0.7) = 7.5 mi/hr

Using the general form :

• y = bx + c

At, x = 1.2 hours ;

Miles left, y = 6 miles

End point decreases by 7.5 mi/hr (-7.5 mi/hr)

Inputting the data into the equation :

6 = - 7.5(1.2) + c

6 = - 9 + c

c = 6 + 9 = 15 miles

The expression in slope intercept form becomes ;

• y = -7.5x + 15

If Raul lives 5 miles closer to the beach ;

Time it will take Luis to get to the beach :

• Time taken = (15 ÷ 7.5) = 2.5 hours

Distance Raul has to cover = 15 - 5 = 10 miles

To reach the beach after 2.5 hours ;

• Speed required = (10 ÷ 2.5) = 4 mi/hr

Therefore, Raul has to ride at 4 miles per hour for the plan to work.

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