the teacher is wrong!! what do you think?

Question

the bad guy beats up hero and ties him up. he jumps on his horse and goes 25mph. after 15 mins, the hero frees himself and takes off at 30 mph. how long before the hero catches bad guy, assuming horses don't get tired....
a. 2.21 hours
b. 1.25 hours
c. 75 minutes
d. both b and c

but it is 1.5 hours is it not/??

Answer 1

I think that you are misinterpreting the question. As written the problem is ambiguous.

The question you are supposed to answer is "How long before the hero catches the bad guy?"

You might reasonably ask "How long since *when*?"

If you mean "How long since the hero was tied up," then the answer is indeed 1.5 hours.

But if you mean "How long after the hero frees himself," then the answer is 1.25 hours.

So, if we interpret "How long" to mean "How long after the hero frees himself," then the answer is (d), because (b) and (c) both refer to the same length of time (1.25 hours = 75 minutes).

(If the question you answered actually had this wording, and did not specify what "how long" meant, then you should complain to your teacher that the problem has an ambiguous wording.)

Answer 2

lead is 15 min at 25 mph = 25/4 miles
range rate is 5 mph 30 -25 , the rate two objects are approaching

so how much time to go 25/4 miles at 5 mph
the naswer is (25/5) /4 = 5/4 hours or 1 hour 15 minutes
answer b 1.25 hours

Note: if you are not careful you calculate the time from when the bad guy departs, rather than 15 minutes later when the good guy starts .

The good guy takes 1.25 hours from when he starts riding until he catches the bad guy, but that is 1.5 hours from when the bad guy leaves 1.25 + .25 hours = 1.5

Answer 3

Nope its 1.25 hours

ok here's how i worked it out

Calculate how far the bad guy is ahead when the hero finally manages to untie himself. The answer is (25mph /4) u divide by 4 since 15minutes is one quarter of an hour, hence the bad guy is 25/4miles ahead of the hero initially.

Now change ur way of thinking. Since the bad guy is travelling at 25mph and the hero is travelling at 30mph, isn't it basically saying that the hero is travelling 5mph faster than the bad guy. So basically, every hour that passes by, the hero catches up by 5miles

so u divide 25/4 miles (i.e. 6.25miles) by 5miles and u get 1.25 -- that is the time in hours it takes for the hero to catch up

hope that helps

Answer 4

bad guy has a head start of 25/4 miles= 6.25 miles

So if they meet x hrs later then

30 * x = 6.25 + 25* x
Solve for x
5x=6.25
x=1.25 hrs or 1 hour 15 min or 75 min

Your teacher is not wrong! Pick D

Answer 5

The answer is d. 1.25 hrs and 75 min

Explanation: After 15 min, BG has gone 6.25 miles. In the next 1.25 hr, he goes 31.25 miles. Total miles = 37.5, total time doesn't count head start so it is 1.25 hours. At 30 MPH, Hero goes 37.5 miles in 1.25 hrs.
1.25 hrs = 75 minutes

Answer 6

The distance when he frees himself is 25mph x (0.25hr) = 6.25mi.

The difference in speed, (relative speed) is 5 mph.

time = distance/speed

time = 6.25/5 = 1.25 hrs, or 60min + 15min = 75min.

Answer 7

The bad guy's position as a function of time is
x1 = (25 mile/hr)*t

The good guy's position as a function of time is zero until fifteen minutes (0.25 hours) into the chase, at which point it is:
x2 = (30 mile/hr)*(t - 0.25 hr)

The good guy catches the bad guy when x2 reaches x1:
x1 = x2
(25 mile/hr)*t = (30 mile/hr)*(t - 0.25 hr)
(25 mile/hr)*t = (30 mile/hr)*t - (30 mile/hr)*(0.25 hr)
(5 mile/hr)*t = (30 mile/hr)*(0.25 hr)
t = 6*(0.25 hr)
t = 1.5 hr

You are correct.

Answer 8

it is b, 1.25 hours. here is the equation:
25*x+6.25 = 30*x

the 6.25 comes from 15min * 1hr/60min * 25 mph = 6.25 miles

Answer 9

The Answer is D!
25(1x+.25) = 30(x)
25x+6.25 = 30x
6.25 = 5x
x=1.25hr (or 75min)

Answer 10

It is not 1.5 hours. Check your calculation again.