Math Help - Distance problems

Hello,

These are some SAT prep problems that I'm not sure about...

How long would a 1000 mile trip take if I was traveling at 50 mph for the first 500 miles and 60 mph for the rest of the trip?

A boat can reach its destination in 3 hours. If it goes twice as fast as it can reach 10 miles more than its destination, in 2 hours. How fast does it originally go?

A man can drive a certain distance in 5 hours. If he increased his speed by 10 mph, he could travel the same distance in 25/6 hours. What is the distance he travels?

Originally Posted by m58

How long would a 1000 mile trip take if I was traveling at 50 mph for the first 500 miles and 60 mph for the rest of the trip?

For the first 500 miles at 50 mph implies h = 500/50 = 10 hours, for the second 500 miles at 60 mph implies h = 500/60 = 8.33 hours.

Do you follow?

Similar logic applies to the 2nd and 3rd questions, have a go!

Ah, that's far easier than how I originally tried it! Thanks!

For the second problem, I did:
D = RT
3R = (R)(3)
D + 10 = (2R)(2)
D = 4R - 10
Input (4R - 10) into the first equation to get: 3 = 4R - 10/R -> 3R = 4R - 10 -> 10 = R

For the third problem, how's this answer: 500/4 = 125, so his distance will be 125 more mph than before

Originally Posted by m58

Hello,
A man can drive a certain distance in 5 hours. If he increased his speed by 10 mph, he could travel the same distance in 25/6 hours. What is the distance he travels?

since the distance is the same and we are just adusting the rate you have



or



thus

so initially if the trip took hours at then the distance was miles
so if you add

this matches the hours