The smith family is going on a five day journey. On tuesday the cover 7 over 24 of the total distance, on Wednesday 11 over 48 on Thursday 3 over 16 and on Friday 1 over 8.
a). What percentage of the journey do they cover on Thursday?
b). What fraction of the total distance do they have to cover on Saturday.
c). The distance they will cover on the journey is 900 km. How many kilometres did they cover on Teusday?
LCD is 48
tuesday 14/48
wed 11/48
thurs 9/48
fri 6/48
total so far = 40/48
a) (9/48)100 = 18.75 %
b) 48/48 - 40/48 = 8/48 = 1/6
c) (7/24)900 = 262.5 km
a) To find the percentage of the journey they cover on Thursday, we need to add up the fractions for each day's distance covered and then convert that into a percentage.
On Tuesday, they cover 7/24 of the total distance.
On Wednesday, they cover 11/48 of the total distance.
On Thursday, they cover 3/16 of the total distance.
On Friday, they cover 1/8 of the total distance.
To add up the fractions, we need to find a common denominator. The least common denominator for 24, 48, and 16 is 48. So, let's convert each fraction to have a denominator of 48:
Tuesday: (7/24) x (2/2) = 14/48
Wednesday: (11/48) x (1/1) = 11/48
Thursday: (3/16) x (3/3) = 9/48
Friday: (1/8) x (6/6) = 6/48
Now, add up the fractions: 14/48 + 11/48 + 9/48 + 6/48 = 40/48.
To convert this to a percentage, divide 40 by 48 and multiply by 100:
(40/48) x 100 ≈ 83.33%
Therefore, they cover approximately 83.33% of the journey on Thursday.
b) To find the fraction of the total distance they have left to cover on Saturday, we need to subtract the sum of the fractions covered on Tuesday, Wednesday, Thursday, and Friday from 1 (which represents the whole).
On Tuesday, they cover 7/24 of the total distance.
On Wednesday, they cover 11/48 of the total distance.
On Thursday, they cover 3/16 of the total distance.
On Friday, they cover 1/8 of the total distance.
To add up the fractions, we need to find a common denominator. The least common denominator for 24, 48, and 16 is 48. So, let's convert each fraction to have a denominator of 48:
Tuesday: (7/24) x (2/2) = 14/48
Wednesday: (11/48) x (1/1) = 11/48
Thursday: (3/16) x (3/3) = 9/48
Friday: (1/8) x (6/6) = 6/48
Now, add up the fractions: 14/48 + 11/48 + 9/48 + 6/48 = 40/48.
To find the fraction they have left to cover, subtract 40/48 from 1:
1 - 40/48 = 8/48.
Therefore, they have 8/48 or 1/6 of the total distance left to cover on Saturday.
c) Since we know that they cover 7/24 of the total distance on Tuesday, we can find the distance they covered on Tuesday by multiplying this fraction by the total distance.
Total distance = 900 km
Distance covered on Tuesday = (7/24) x 900 = (7/24) x (900/1) = 7 x 900 / 24 = 262.5 km.
Therefore, they covered approximately 262.5 km on Tuesday.
To solve these problems, we'll need to calculate the percentages and fractions based on the distances covered each day.
a) To find the percentage of the journey covered on Thursday, divide the distance covered on Thursday by the total distance and multiply by 100.
Distance covered on Thursday = 3/16 of the total distance
Percentage covered on Thursday = (3/16) * 100
To calculate this, multiply the fraction by 100 and express it as a percentage.
Percentage covered on Thursday = (3/16) * 100 = 18.75%
Therefore, they cover 18.75% of the journey on Thursday.
b) To find the fraction of the total distance they have to cover on Saturday, subtract the cumulative distance covered from the total distance.
Cumulative distance covered = (7/24) + (11/48) + (3/16) + (1/8) of the total distance
To simplify this, find a common denominator and add the fractions.
Cumulative distance covered = (14/48) + (11/48) + (9/48) + (6/48)
Cumulative distance covered = 40/48
To find the remaining fraction of the total distance they have to cover on Saturday, subtract the cumulative distance covered from 1 (whole distance).
Fraction left to cover on Saturday = 1 - (40/48)
Fraction left to cover on Saturday = (48/48) - (40/48)
Fraction left to cover on Saturday = 8/48
Therefore, they have 8/48 (or simplified as 1/6) of the total distance left to cover on Saturday.
c) If the total distance of the journey is 900 km, we can calculate the distance covered on Tuesday by using the fraction provided and multiplying it by the total distance.
Distance covered on Tuesday = (7/24) * 900
Distance covered on Tuesday = (7 * 900) / 24
Distance covered on Tuesday = 2,100 / 24
Distance covered on Tuesday = 87.5 km
Therefore, they covered 87.5 km on Tuesday.