The distance from the south entrance to the north entrance of a certain straight bicycling trail is 88 miles. At 11:00 AM, Zelda starts biking from the north entrance towards the south entrance of the trail. At 1:00 PM, Frank starts biking from the south entrance towards the north entrance of the trail. If Zelda is biking at a constant rate of 8 miles per hour and Frank is biking at a constant rate of 10 miles per hour, how many miles will Zelda have biked when she passes Frank on the trail?
(a) 48
(b) 46
(c) 44
(d) 42
(e) 41
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rate problem using the chart/box method?
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I will take a stab... I hope i'm right:
rate x time = distance
zelda 8 x t +2 = 8t + 16
frank 10 x t = 10t
total - x - = 88
Therefore 18t + 16 = 88
t = 4 hours... therefore zelda travels 4 + 2 hours 6 hours for a total of 48 miles when they are equal
rate x time = distance
zelda 8 x t +2 = 8t + 16
frank 10 x t = 10t
total - x - = 88
Therefore 18t + 16 = 88
t = 4 hours... therefore zelda travels 4 + 2 hours 6 hours for a total of 48 miles when they are equal
I could be wrong but I don't think you will ever have a negative time. So whoever starts later is always going to be the t and then you just add the assoicated difference.jzw wrote:that's correct - what was tripping me up was I was putting zelda's time as X and frank's time as t-2. can you tell me what signaled to you to make zelda's +2 instead of frank's -2?
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From 11am to 1pm, the distance traveled by Zelda = r*t = 8*2 = 16 miles.jzw wrote:The distance from the south entrance to the north entrance of a certain straight bicycling trail is 88 miles. At 11:00 AM, Zelda starts biking from the north entrance towards the south entrance of the trail. At 1:00 PM, Frank starts biking from the south entrance towards the north entrance of the trail. If Zelda is biking at a constant rate of 8 miles per hour and Frank is biking at a constant rate of 10 miles per hour, how many miles will Zelda have biked when she passes Frank on the trail?
(a) 48
(b) 46
(c) 44
(d) 42
(e) 41
Remaining distance between Zelda and Frank = 88-16 = 72 miles.
When elements travel TOWARD EACH OTHER, they WORK TOGETHER to cover the distance between them, so we ADD THEIR RATES.
Time for Zelda and Frank to travel 72 miles = d/r = 72/(8+10) = 4 hours.
Distance traveled by Zelda in 4 hours = r*t = 8*4 = 32 miles.
Total distance traveled by Zelda = 16+32 = 48 miles.
The correct answer is A.
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jzw
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I wish I could think like you do Mitch! You see these questions and you make a "tough" rate problem look like it's really a simple logic question. Like - of course Zelda's traveled 16 miles by 1pm, and since they're traveling towards each other we all know to combine the rates for the remaining distance, which is 72 miles, so 72/18=4 hours, then take 4*8=32+16=48. I wish I could see these questions the way you do. If only I had another 2 months to study...
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spartacus1412
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option A
Z bikes at 8mph from 11 to 1 (2 hrs)it bikes 16 kms.
now the distance remaining to be covered is 88-16 = 72
now jack starts biking at 10 mph.
hence the total time elapsed before both Z and jack meet is total distance left/total relative speed
time before both meet is = 72/10+18= 72/4 = 4hr.
hence, both Z and JAck meet after 4 hrs.
hence, distance biked by Z is : distance biked from 11am to 1pm + distance in 4 hrs
16+ 4*8 =16+32 = 48 hrs
Z bikes at 8mph from 11 to 1 (2 hrs)it bikes 16 kms.
now the distance remaining to be covered is 88-16 = 72
now jack starts biking at 10 mph.
hence the total time elapsed before both Z and jack meet is total distance left/total relative speed
time before both meet is = 72/10+18= 72/4 = 4hr.
hence, both Z and JAck meet after 4 hrs.
hence, distance biked by Z is : distance biked from 11am to 1pm + distance in 4 hrs
16+ 4*8 =16+32 = 48 hrs
