Sure! Let's solve each of the problems step-by-step.
### Problem 15:
If [tex]\(\frac{5}{8}\)[/tex] of a rod is equal to 5 metres, what is [tex]\(\frac{3}{4}\)[/tex] of the rod?
We know:
[tex]\[
\frac{5}{8} \text{ of the rod} = 5 \text{ meters}
\][/tex]
To find the entire length of the rod:
[tex]\[
\text{Let the full length of the rod be } L \text{ meters}.
\][/tex]
[tex]\[
\frac{5}{8}L = 5
\][/tex]
[tex]\[
L = 5 \div \frac{5}{8}
\][/tex]
[tex]\[
L = 5 \times \frac{8}{5}
\][/tex]
[tex]\[
L = 8 \text{ meters}
\][/tex]
Now, to find [tex]\(\frac{3}{4}\)[/tex] of the rod:
[tex]\[
\frac{3}{4}L = \frac{3}{4} \times 8 = 6 \text{ meters}
\][/tex]
Thus, [tex]\(\frac{3}{4}\)[/tex] of the rod is 6 meters. Therefore, the answer is:
[tex]\[
\boxed{6}
\][/tex]
### Problem 16:
How long will a man take to walk 600 meters if his walking rate is 4 km per hour?
First, convert the walking rate from kilometers per hour to meters per minute:
[tex]\[
4 \text{ km/hr} = 4 \times 1000 \text{ meters/hr} = 4000 \text{ meters/hr}
\][/tex]
[tex]\[
4000 \text{ meters/hr} = 4000 \div 60 \text{ meters/minute} = \frac{4000}{60} \text{ meters/minute} = 66.67 \text{ meters/minute}
\][/tex]
Now, calculate the time taken to walk 600 meters:
[tex]\[
\text{Time} = \frac{600 \text{ meters}}{66.67 \text{ meters/minute}} \approx 9 \text{ minutes}
\][/tex]
Therefore, the time taken to walk 600 meters is:
[tex]\[
\boxed{9 \text{ minutes}}
\][/tex]
### Problem 17:
A man can do [tex]\(\frac{7}{8}\)[/tex] of a piece of work in 35 days; how long will it take to do 60% of it?
First, find the total amount of time required to complete the entire work:
[tex]\[
\text{Let the total work be } W.
\][/tex]
[tex]\[
\frac{7}{8}W = \text{ work done in 35 days}
\][/tex]
[tex]\[
\frac{7}{8}W = 35 \text{ days}
\][/tex]
[tex]\[
W = 35 \div \frac{7}{8}
\][/tex]
[tex]\[
W = 35 \times \frac{8}{7}
\][/tex]
[tex]\[
W = 40 \text{ days}
\][/tex]
Now, calculate the time to complete 60% of the work:
[tex]\[
\text{Time for 60% work} = 40 \times \frac{60}{100}
\][/tex]
[tex]\[
= 40 \times 0.6 = 24 \text{ days}
\][/tex]
Therefore, the man will take:
[tex]\[
\boxed{24 \text{ days}}
\][/tex]
