Andrea has 1 hour to spend training for an upcoming race. She completes her training by running full speed the distance of the race and walking back the same distance to cool down. If she runs at a speed of 7mph and walks back at a speed of 3 mph, how long should she plan to spend walking back?

Question

Andrea has 1 hour to spend training for an upcoming race.  She completes her training by running full speed the distance of the race and walking back the same distance to cool down.  If she runs at a speed of 7mph and walks back at a speed of 3 mph, how long should she plan to spend walking back?

anonymous · Answer

is this all the info?

amistre64 · Answer

d = s*t

its a ratio of 7/3,  or is it 3/7?

anonymous · Answer

yeah this is a;ll the information

amistre64 · Answer

d = 7n
d = 3m

7n = 3m

m = 7n/3 ; so it seems to depend on another bit of info if i see it right

amistre64 · Answer

maybe we derive the distance by equating the full time out to be an hour and divvy the time between run and walk?

anonymous · Answer

this is a brain tingler
is there anyway we can use ratios?

anonymous · Answer

i dont think so....  it is just asking for the number of hours

amistre64 · Answer

assume we know the distance; say 528 miles; how would it solve then?

amistre64 · Answer

...  28 miles lol

anonymous · Answer

haha

anonymous · Answer

mmm we cooould

amistre64 · Answer

get a particular solution and work it into a general :)

amistre64 · Answer

7*3 = 21; so try that :)

anonymous · Answer

okay wait
i got it

anonymous · Answer

i think

anonymous · Answer

the speed ratio is 7:3

anonymous · Answer

so shouldnt the time also be 7:3

anonymous · Answer

or 3:7?

anonymous · Answer

60 = m + n 
7 * m = 3 * n
solve this

amistre64 · Answer

that looks plausible

anonymous · Answer

i have no idea...  i am lost

amistre64 · Answer

18 min running and 42 minutes walking  sounds good :)

anonymous · Answer

60-n = m
7 * m = 3n
7(60-n) = 3 n
420-7n = 3n
420 = 3n+7n 
420 = 10n
42 = n
m = 60-42 = 18
7 * 18/60 =  2.1 miles
3 * 42/60 = 2.1 miles

anonymous · Answer

there should be it

anonymous · Answer

yeah thats what i was thinking. u agree amistre?

amistre64 · Answer

i agree :)

anonymous · Answer

sweets. how is that kelly?

anonymous · Answer

so the correct answer is 2.1 miles?

amistre64 · Answer

lol ... distance isnt time

anonymous · Answer

arent you looking for time?

anonymous · Answer

its 42 minutes walking back

amistre64 · Answer

time running = 18 and time walking = 42

distance of race = 2.1 maybe

anonymous · Answer

whoops....  i got confused...  it is asking for hours

anonymous · Answer

well, it the question it states that she have one hour to practise in, so the answer should be 42 minutes as far as i can see.