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mand-y
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TWO distance problems 15 Jun 2006, 17:24
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:) help needed plz explain your reasoning and equations
thanks
Greg leaves home for Franklin 400 miles away. After 2 hours, he has to reduce his speed by 20 mph due to rain. If he takes 1 hour for lunch and gas, and reaches Franklin 9 hours after he left home, what was his initial speed?
. Bill left Rome at 8am and drove his Ferrari at 80 mph from Rome to Sorrento. He then took the boat to Capri for the day, returning to Sorrento 5 hours later. On the return trip from Sorrento to Rome he averaged 60 mph and arrived at 8pm. How far is it from Rome to Sorrento?

0A

1) 65 mph FIRST ONE

2) 240 miles SECOND ONE

THANKS



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haas_mba07
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TWO distance problems 15 Jun 2006, 17:34
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These should be pretty straight forward
Making equations out of the word problems usually helps.

1. d = 400 (given)

Let s be the original speed.
Travel 2 hrs @ s miles/hr distance covered = sx2

Speed reduced by 20mph, new speed = s-20
Travel 6 hrs @ (s-2) miles/hr, distance = (s-20)x6

As total distance = 400

sx2 + (s-20)x6 = 400
8s = 520 => s = 65mph

2. total time taken = 12 hrs
Let distance = d

As time = distance/speed
time for travel distance d @ 80mph = d/80
time for travel distance d @ 60mph = d/60
Additional time on boat and back +day = 5hrs

Sum of all above = 12 i.e.

d/80 + d/60 + 5 = 12

d/8 + d/6 = 70

or 14d/48 = 70 => d = 240miles
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ywilfred
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TWO distance problems 15 Jun 2006, 18:38
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Original speed = x, after two hours, he would have covered 2x miles.

So (400-2x) miles was covered at a speed of (x-20) mph

Time = 9 hours = 1 + 2 + (400-2x)/(x-20)

6 = 400-2x/(x-20)

8x = 520

x = 65
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ywilfred
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TWO distance problems 15 Jun 2006, 18:44
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Distance between Rome + Sorrento = x miles

Time taken to get from Rome to Sorrento = x/80 hours

Time taken to travel from Sorrento to Rome = x/60 hours

8am to 8pm = 12 hours

x/80 + x/60 + 5 = 12

(3x + 4x)/240 = 7

7x = 7(240)
x = 240 miles
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jaynayak
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TWO distance problems 15 Jun 2006, 23:51
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1) Here we know the total distance hence we have to form a equation based on distance.

Let x be the intiial speed.
Hence distance travelled in 2 hrs = 2x
Total time taken = 9
Time for lunch = 1 hr
Time taken in intital speed = 2
Remainng time = 6
Speed for remaining time = x-2
Distance traveled in speed X-2 = 6(x-2)

Hence 400 = 2x + 6(x-2)
520 = 8x
x = 65

2) Here we know the total time taken (=12hrs) hence the equation to formed should be based on time.
Let distance bet R-S is x kms
Time taken from R-S = x/80 hrs
Time taken in Capri = 5 hrs
Time taken in return trip = x/60

Hence,

x/80 + 5 + x/60 = 12
7x/240 = 7
x = 240
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TWO distance problems 16 Jun 2006, 00:20
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#1. Disregard 1 hr of lunch coz it means no change in displacement.

so we get -
400 = 2x + 6(x - 20); where x = speed in mph
=> x = 65 mph

#2. Disregard 5 hrs of Sorrento to Capri and back, coz it represents no change in displacement as far as we are concerned (that is because we are measuring Sorrento to Rome, Capri not included).

We get -
80t = 60(7 - t); where t = time taken; 7 = 12 (total time) - 5 (sorrento to capri and back)
=> t = 3
=> distance b/w rome and sorrento = 240 miles

:shock: I thought Sorrento was near Melbourne!



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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