Please help! t(r)= d/r t=time in hours, d=distance, r=rate in mi/h Sydney drives 10 mi at a certain rate and then drives 20 mi at a rate 5 mi/h faster than the initial rate. Write expressions for the time along each part of the trip. Add these times to write an equation for the total time in terms of initial rate, t Total (r).

Question

anonymous · Answer

$$\frac{10}{r}+\frac{20}{r+5}=\frac{30 r+50}{r^2+5 r} $$

anonymous · Answer

r+5 is the rate for when she drives 20 miles.

anonymous · Answer

Yes.

anonymous · Answer

Okay so what you put is the final answer correct?

anonymous · Answer

Yes, either side of the equation answers the question.  The RHS is the result of combining the two fractions.

anonymous · Answer

Oh! Okay, good that is the same answer I got on my own, I just wanted to check it. Could you help me with the next part by any chance? It asks "At what rate, to the nearest mi/h, must Sydney drive for the first 10 miles if the entire 30 miles must be covered in about 45 minutes?

anonymous · Answer

45 minutes is 3/4 ths of an hour.  Solve the following for r:$$\frac{10}{r}+\frac{20}{r+5}=\frac{3}{4} $$$$r=\frac{5}{6} \left(21+\sqrt{537}\right)=37 \text{ mph} \text{ rounded} $$

anonymous · Answer

Thank you so much! Lastly, "How long will it take Sydney to drive the entire 30 miles if the car's initial rate varies between 10 mi/h and 20 mi/h?

anonymous · Answer

The average speed is 30/2 or 15 mph.$$\frac{10 (3 r+5)}{r (r+5)}  $$evaluated at r = 15 is 5/3 hour or 1 hour and 40 minutes

anonymous · Answer

At a constant speed of 10 mph and 20 mph, the total trip time would be 7/3 and 13/10 hours respectively.

anonymous · Answer

Thank you so much for your help!

anonymous · Answer

You're welcome.